title

Machine Learning for Fluid Mechanics

description

@eigensteve on Twitter
This video gives an overview of how Machine Learning is being used in Fluid Mechanics. In fact, fluid mechanics is one of the original "big data" sciences, and many advances in ML came out of fluids.
Read the paper: https://www.annualreviews.org/doi/abs/10.1146/annurev-fluid-010719-060214
Free Arxiv paper: https://arxiv.org/abs/1905.11075
Citable link for this video: https://doi.org/10.52843/cassyni.27tbdb
Lab website: www.eigensteve.com

detail

{'title': 'Machine Learning for Fluid Mechanics', 'heatmap': [{'end': 857.427, 'start': 810.172, 'weight': 1}, {'end': 1266.583, 'start': 1237.17, 'weight': 0.741}], 'summary': 'Delves into the increasing role of machine learning in fluid mechanics, emphasizing its impact on technological advancements and the connection between machine learning and fluid optimization. it also explores the need for interpretable and generalizable models in fluid dynamics, the historical relationship between machine learning and fluid mechanics, and the application of machine learning in turbulent fluid dynamics, closure modeling, super-resolution technology, and real-time feedback control.', 'chapters': [{'end': 247.784, 'segs': [{'end': 110.794, 'src': 'embed', 'start': 69.98, 'weight': 0, 'content': [{'end': 75.341, 'text': 'where we have such vast and increasing amounts of data from simulations and from experiments.', 'start': 69.98, 'duration': 5.361}, {'end': 77.882, 'text': "And so I'm going to walk you through, at a very high level,", 'start': 75.841, 'duration': 2.041}, {'end': 83.383, 'text': 'some of my favorite examples and applications of how machine learning is being used for fluid mechanics today.', 'start': 77.882, 'duration': 5.501}, {'end': 94.349, 'text': 'Good. So I want to start by kind of just walking you through what I think of when I think of machine learning, especially applied to engineering systems.', 'start': 84.864, 'duration': 9.485}, {'end': 97.43, 'text': 'So fluid mechanics are absolutely everywhere.', 'start': 94.949, 'duration': 2.481}, {'end': 105.132, 'text': 'Fluids play a central role in nearly every trillion-dollar industry, health, defense, transportation, energy.', 'start': 97.53, 'duration': 7.602}, {'end': 110.794, 'text': 'We literally live and work inside of a fluid, and so do all of our machines.', 'start': 105.712, 'duration': 5.082}], 'summary': 'Machine learning applied to fluid mechanics in various trillion-dollar industries.', 'duration': 40.814, 'max_score': 69.98, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw69980.jpg'}, {'end': 188.4, 'src': 'embed', 'start': 160.906, 'weight': 4, 'content': [{'end': 164.507, 'text': 'can very naturally be written as hard optimization problems.', 'start': 160.906, 'duration': 3.601}, {'end': 168.528, 'text': 'Okay, so these optimization problems in fluids are very challenging.', 'start': 164.827, 'duration': 3.701}, {'end': 171.029, 'text': "That's why it's hard to make progress in these fields.", 'start': 168.548, 'duration': 2.481}, {'end': 172.169, 'text': "That's why they're so important.", 'start': 171.069, 'duration': 1.1}, {'end': 177.99, 'text': 'These optimizations are nonlinear, nonconvex, multiscale, very high dimensional.', 'start': 173.429, 'duration': 4.561}, {'end': 183.355, 'text': 'But I want to point out that that is exactly what machine learning is getting really good at.', 'start': 178.611, 'duration': 4.744}, {'end': 188.4, 'text': 'So if I want to pigeonhole or kind of make a blanket statement about machine learning,', 'start': 183.575, 'duration': 4.825}], 'summary': 'Fluid optimization problems are challenging, but machine learning excels in solving them.', 'duration': 27.494, 'max_score': 160.906, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw160906.jpg'}, {'end': 234.055, 'src': 'embed', 'start': 206.158, 'weight': 3, 'content': [{'end': 209.08, 'text': 'Okay, so machine learning is optimization with data,', 'start': 206.158, 'duration': 2.922}, {'end': 214.024, 'text': 'and most of the problems that we have in fluid mechanics can be very naturally written as optimization problems.', 'start': 209.08, 'duration': 4.944}, {'end': 217.166, 'text': 'So these go together extremely naturally,', 'start': 214.604, 'duration': 2.562}, {'end': 224.712, 'text': "and what we're gonna see is that lots and lots of techniques for machine learning can be directly applied to solving these fluids optimization problems like modeling,", 'start': 217.166, 'duration': 7.546}, {'end': 226.454, 'text': 'control, sensing and so on.', 'start': 224.712, 'duration': 1.742}, {'end': 234.055, 'text': 'And I want to point out, when I say high dimensional, I mean that the fluid flow itself has many, many, many degrees of freedom.', 'start': 227.17, 'duration': 6.885}], 'summary': 'Machine learning techniques can be applied to fluid mechanics optimization problems, leveraging high-dimensional fluid flow data.', 'duration': 27.897, 'max_score': 206.158, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw206158.jpg'}], 'start': 7.059, 'title': 'Machine learning in fluid mechanics and optimization', 'summary': 'Discusses the rising role of machine learning in fluid mechanics, emphasizing its impact on technological advancements. it also highlights the natural connection between machine learning and fluid optimization, showcasing its ability to excel at building models from data using optimization techniques for highly challenging fluid optimization problems.', 'chapters': [{'end': 160.906, 'start': 7.059, 'title': 'Machine learning for fluid mechanics', 'summary': 'Discusses the increasing role of machine learning in fluid mechanics, highlighting its applications and potential impact on technological advancements, especially in the physical sciences and engineering.', 'duration': 153.847, 'highlights': ['Machine learning is making significant advances in the field of artificial intelligence and especially in image sciences, enabling tasks like turning a static image into a movie. This technology has potential applications in physical sciences and engineering, particularly in fluid mechanics.', 'Fluid mechanics, being crucial in trillion-dollar industries like health, defense, transportation, and energy, presents critical tasks such as model reduction, controlling fluid flows, sensor placement, and closure models, all of which are essential for solving future technological challenges.', 'The utilization of machine learning for fluid mechanics holds the potential to enable advancements in energy systems, transportation systems, and other technological developments, emphasizing the central role of fluids in these domains.']}, {'end': 247.784, 'start': 160.906, 'title': 'Machine learning for fluid optimization', 'summary': 'Highlights the natural connection between machine learning and fluid optimization, emphasizing that machine learning excels at building models from data using optimization techniques, which aligns with the highly challenging and high-dimensional nature of fluid optimization problems.', 'duration': 86.878, 'highlights': ['Machine learning excels at building models from data using optimization, making it well-suited for the challenging and high-dimensional nature of fluid optimization problems.', 'Fluid optimization problems are nonlinear, nonconvex, multiscale, and very high dimensional, with the need for a million or billion degrees of freedom to simulate turbulent fluid in a computer.', 'The natural connection between machine learning and fluid optimization suggests that techniques for machine learning can be directly applied to solving fluid optimization problems like modeling, control, and sensing.']}], 'duration': 240.725, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw7059.jpg', 'highlights': ["Machine learning's potential applications in physical sciences and engineering, particularly in fluid mechanics.", "Fluid mechanics' crucial role in trillion-dollar industries like health, defense, transportation, and energy.", 'Utilization of machine learning for fluid mechanics holds potential to enable advancements in energy and transportation systems.', 'Machine learning excels at building models from data using optimization, making it well-suited for fluid optimization problems.', 'Fluid optimization problems are nonlinear, nonconvex, multiscale, and very high dimensional.', 'The natural connection between machine learning and fluid optimization suggests direct application of machine learning techniques.']}, {'end': 590.899, 'segs': [{'end': 363.898, 'src': 'embed', 'start': 333.476, 'weight': 0, 'content': [{'end': 337.559, 'text': 'And so instead of kind of rigorously defining what I mean by these, I want to give you an example.', 'start': 333.476, 'duration': 4.083}, {'end': 344.905, 'text': "So I think of Newton's second law, F equals ma, as the ultimate interpretable and generalizable model.", 'start': 338.42, 'duration': 6.485}, {'end': 347.147, 'text': "It's interpretable because it's very simple.", 'start': 345.206, 'duration': 1.941}, {'end': 350.77, 'text': "It's in terms of force, mass, and acceleration.", 'start': 347.167, 'duration': 3.603}, {'end': 358.116, 'text': "And it's generalizable in the sense that Newton can discover this law from an apple falling on a tree on Earth.", 'start': 351.451, 'duration': 6.665}, {'end': 363.898, 'text': 'And this law still works when we design a rocket mission from the Earth to the Moon.', 'start': 358.977, 'duration': 4.921}], 'summary': "Newton's second law, f=ma, is a simple and generalizable model that applies to rocket missions from earth to the moon.", 'duration': 30.422, 'max_score': 333.476, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw333476.jpg'}, {'end': 441.152, 'src': 'embed', 'start': 413.432, 'weight': 2, 'content': [{'end': 418.554, 'text': "low dimensional, so they're not in terms of a million degrees of freedom like a fluid dynamic simulation would be.", 'start': 413.432, 'duration': 5.122}, {'end': 423.936, 'text': 'And we want them to be robust in lots of ways robust to noise and disturbances,', 'start': 419.194, 'duration': 4.742}, {'end': 430.659, 'text': "robust to bad information that goes into the training and robust to new scenarios that we haven't seen before.", 'start': 423.936, 'duration': 6.723}, {'end': 435.101, 'text': 'Okay, so this is what we want in kind of machine learning for fluid mechanics in general.', 'start': 430.959, 'duration': 4.142}, {'end': 441.152, 'text': "Now I want to point out a lot of what I'm going to talk about in this video and in future.", 'start': 436.408, 'duration': 4.744}], 'summary': 'Desire low-dimensional, robust machine learning for fluid mechanics.', 'duration': 27.72, 'max_score': 413.432, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw413432.jpg'}, {'end': 486.714, 'src': 'embed', 'start': 456.627, 'weight': 1, 'content': [{'end': 460.633, 'text': "So here's a figure that didn't make it into the review, but I like this figure a lot.", 'start': 456.627, 'duration': 4.006}, {'end': 467.181, 'text': 'And it kind of at a very high level points out that fluid dynamics generates tremendous amounts of data.', 'start': 460.673, 'duration': 6.508}, {'end': 472.609, 'text': 'So we have theory, simulations, and experiments that are kind of generating this fluid dynamics data.', 'start': 467.462, 'duration': 5.147}, {'end': 478.512, 'text': 'And machine learning can be thought of as this common information processing framework,', 'start': 473.91, 'duration': 4.602}, {'end': 486.714, 'text': 'so that you can integrate this flow data and use that to start solving these really hard optimization problems in modeling and control and reduction.', 'start': 478.512, 'duration': 8.202}], 'summary': 'Fluid dynamics generates massive data; machine learning integrates and uses it for solving optimization problems.', 'duration': 30.087, 'max_score': 456.627, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw456627.jpg'}], 'start': 248.484, 'title': 'Machine learning in fluid dynamics and mechanics', 'summary': 'Emphasizes the importance of interpretable and generalizable machine learning models in fluid dynamics, highlighting the need for trustable models that can work in new situations. it also discusses the historical connection of machine learning with fluid mechanics as highlighted in a 2020 review paper.', 'chapters': [{'end': 412.512, 'start': 248.484, 'title': 'Machine learning in fluid dynamics', 'summary': "Discusses the importance of interpretable and generalizable machine learning models in fluid dynamics, emphasizing the need for models that are not black boxes and can be trusted to work in new situations, using newton's second law as an example.", 'duration': 164.028, 'highlights': ['The importance of interpretable and generalizable machine learning models in fluid dynamics is emphasized, highlighting the need for models that are not black boxes and can be trusted to work in new situations.', "The example of Newton's second law, F equals ma, is used to illustrate the ultimate interpretable and generalizable model, which covers a range of phenomena, even those not seen before.", 'The misconception that machine learning is like a magic wand is addressed, emphasizing that it is very understandable in terms of linear algebra, optimization, and statistics.']}, {'end': 590.899, 'start': 413.432, 'title': 'Machine learning for fluid mechanics', 'summary': 'Discusses the importance of robustness in machine learning for fluid mechanics, its common information processing framework, and the historical connection of machine learning with fluid mechanics, as highlighted in the review paper from 2020.', 'duration': 177.467, 'highlights': ['Fluid dynamics generates tremendous amounts of data from theory, simulations, and experiments, making it a critical area for the integration of machine learning to solve optimization problems in modeling, control, and reduction. Fluid dynamics generates large volumes of data from theory, simulations, and experiments, making it crucial to integrate machine learning for solving optimization problems in modeling, control, and reduction.', 'The review paper from 2020 emphasizes the importance of robustness in machine learning for fluid mechanics, aiming for low-dimensional models that are robust to noise, disturbances, bad information, and new scenarios. The review paper from 2020 stresses the significance of robustness in machine learning for fluid mechanics, aiming for low-dimensional models that are robust to noise, disturbances, bad information, and new scenarios.', 'Fluid mechanics is one of the original fields where machine learning grew out of, with tons of big data and the development of computational architectures and algorithms specifically to handle fluid problems. Fluid mechanics is one of the original fields where machine learning emerged, with abundant big data and the development of computational architectures and algorithms tailored for fluid problems.']}], 'duration': 342.415, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw248484.jpg', 'highlights': ["The example of Newton's second law, F equals ma, is used to illustrate the ultimate interpretable and generalizable model, which covers a range of phenomena, even those not seen before.", 'Fluid dynamics generates tremendous amounts of data from theory, simulations, and experiments, making it a critical area for the integration of machine learning to solve optimization problems in modeling, control, and reduction.', 'The review paper from 2020 emphasizes the importance of robustness in machine learning for fluid mechanics, aiming for low-dimensional models that are robust to noise, disturbances, bad information, and new scenarios.']}, {'end': 987.888, 'segs': [{'end': 647.626, 'src': 'embed', 'start': 613.589, 'weight': 3, 'content': [{'end': 615.069, 'text': "you know, they're very tightly linked.", 'start': 613.589, 'duration': 1.48}, {'end': 619.691, 'text': 'And so the field of fluid mechanics is intrinsically linked to data-driven optimizations.', 'start': 615.309, 'duration': 4.382}, {'end': 629.133, 'text': "There's also this really nice connection to this kind of AI winter in this video by Sir James Lighthill.", 'start': 620.845, 'duration': 8.288}, {'end': 632.356, 'text': "And so I think I'm just gonna play this.", 'start': 629.813, 'duration': 2.543}, {'end': 641.122, 'text': 'This is Sir Lighthill essentially holding some of the leading AI researchers at the time in the 70s on trial.', 'start': 632.496, 'duration': 8.626}, {'end': 647.626, 'text': 'So his argument was that machine learning and artificial intelligence had gone through this massive hype cycle.', 'start': 641.523, 'duration': 6.103}], 'summary': 'Fluid mechanics and data-driven optimizations are intrinsically linked, with a historical connection to ai hype in the 70s.', 'duration': 34.037, 'max_score': 613.589, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw613589.jpg'}, {'end': 686.498, 'src': 'embed', 'start': 664.097, 'weight': 4, 'content': [{'end': 675.567, 'text': 'actually played a pivotal role in the so-called AI winter that really resulted in a massive cut in funding for decades in artificial intelligence research.', 'start': 664.097, 'duration': 11.47}, {'end': 678.79, 'text': "It's kind of ironic and Petros pointed this out,", 'start': 676.808, 'duration': 1.982}, {'end': 686.498, 'text': "I think this is really funny that one of Lighthill's criticisms of AI was that it didn't deliver on natural language processing.", 'start': 678.79, 'duration': 7.708}], 'summary': "Lighthill's criticism led to funding cuts in ai research, impacting natural language processing.", 'duration': 22.401, 'max_score': 664.097, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw664097.jpg'}, {'end': 837.369, 'src': 'embed', 'start': 810.172, 'weight': 2, 'content': [{'end': 815.096, 'text': 'And so a lot of that carries over very directly if you think of your flow field as a picture.', 'start': 810.172, 'duration': 4.924}, {'end': 822.082, 'text': 'And if you think of the time evolution of your flow field as a movie of moving pictures, then a lot of machine learning carries over directly.', 'start': 815.496, 'duration': 6.586}, {'end': 831.244, 'text': 'So one of our kind of go-to algorithms for pulling out patterns in fluid flows is the proper orthogonal decomposition.', 'start': 823.659, 'duration': 7.585}, {'end': 837.369, 'text': 'This is basically a principal components analysis done on flow data where you take a movie of your flow field.', 'start': 831.644, 'duration': 5.725}], 'summary': 'Machine learning applies to flow field analysis, using proper orthogonal decomposition for pattern extraction.', 'duration': 27.197, 'max_score': 810.172, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw810172.jpg'}, {'end': 857.427, 'src': 'heatmap', 'start': 810.172, 'weight': 1, 'content': [{'end': 815.096, 'text': 'And so a lot of that carries over very directly if you think of your flow field as a picture.', 'start': 810.172, 'duration': 4.924}, {'end': 822.082, 'text': 'And if you think of the time evolution of your flow field as a movie of moving pictures, then a lot of machine learning carries over directly.', 'start': 815.496, 'duration': 6.586}, {'end': 831.244, 'text': 'So one of our kind of go-to algorithms for pulling out patterns in fluid flows is the proper orthogonal decomposition.', 'start': 823.659, 'duration': 7.585}, {'end': 837.369, 'text': 'This is basically a principal components analysis done on flow data where you take a movie of your flow field.', 'start': 831.644, 'duration': 5.725}, {'end': 841.972, 'text': 'This is just flow past a cylinder at low Reynolds number 100.', 'start': 837.389, 'duration': 4.583}, {'end': 847.938, 'text': 'And if you subtract off the average flow field and do a singular value decomposition or a principal component analysis,', 'start': 841.972, 'duration': 5.966}, {'end': 857.427, 'text': 'you find that you can very efficiently represent this fluid flow as the sum of only a few kind of eigenflow fields or these proper,', 'start': 847.938, 'duration': 9.489}], 'summary': 'Machine learning applied to fluid flow analysis, using proper orthogonal decomposition on flow data to efficiently represent fluid flow patterns.', 'duration': 47.255, 'max_score': 810.172, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw810172.jpg'}, {'end': 889.001, 'src': 'embed', 'start': 866.738, 'weight': 0, 'content': [{'end': 874.629, 'text': 'So instead of needing a million degrees of freedom if this was a megapixel image, I might only need 10 POD modes and how they vary in time.', 'start': 866.738, 'duration': 7.891}, {'end': 883.494, 'text': 'And so this idea that there are low dimensional patterns in fluids allows you to do really, really powerful things.', 'start': 876.705, 'duration': 6.789}, {'end': 889.001, 'text': 'Essentially take algorithms directly from image processing and apply them to flow data.', 'start': 884.395, 'duration': 4.606}], 'summary': 'Fluid analysis: 10 pod modes instead of 1 million degrees of freedom for megapixel image, enabling powerful algorithm application.', 'duration': 22.263, 'max_score': 866.738, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw866738.jpg'}, {'end': 937.676, 'src': 'embed', 'start': 912.889, 'weight': 1, 'content': [{'end': 919.991, 'text': 'And, using these algorithms, from robust statistics, these kind of modern optimization techniques that leverage patterns in the data,', 'start': 912.889, 'duration': 7.102}, {'end': 924.032, 'text': "she's able to decompose this flow into the true low rank component.", 'start': 919.991, 'duration': 4.041}, {'end': 928.473, 'text': "that's characterized by only a few POD modes and all of that salt and pepper noise.", 'start': 924.032, 'duration': 4.441}, {'end': 935.175, 'text': "So she's able to split the data into kind of the clean data that we want and all of this salt and pepper noise.", 'start': 928.633, 'duration': 6.542}, {'end': 937.676, 'text': 'And this is really very interesting.', 'start': 935.635, 'duration': 2.041}], 'summary': 'Algorithms decompose flow into low-rank component, removing noise. interesting approach.', 'duration': 24.787, 'max_score': 912.889, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw912889.jpg'}], 'start': 591.74, 'title': 'Fluid mechanics, ai winter, and machine learning', 'summary': "Explores the connection between fluid mechanics and data-driven optimizations, the influence of sir james lighthill's criticism on the ai winter, the repercussions of failed ai promises in the 70s, and the role of machine learning, particularly proper orthogonal decomposition, in enhancing the understanding and cleaning of noisy experimental data for better flow estimates.", 'chapters': [{'end': 686.498, 'start': 591.74, 'title': 'Fluid mechanics and ai winter', 'summary': "Discusses the link between fluid mechanics and data-driven optimizations, the impact of sir james lighthill's criticism on the ai winter, and the failed promises of ai in the 70s, leading to a cut in funding for artificial intelligence research.", 'duration': 94.758, 'highlights': ["Sir James Lighthill's criticism led to a cut in funding for artificial intelligence research in the 70s, known as the AI winter.", 'The link between fluid mechanics and data-driven optimizations is a key aspect of research, indicating their intrinsic connection.', "Lighthill's criticism of AI included the failure to deliver on promises such as natural language processing, contributing to the AI winter.", 'Debate at the time about the fit of certain research into the field of fluid mechanics.']}, {'end': 987.888, 'start': 686.859, 'title': 'Machine learning in fluid mechanics', 'summary': 'Discusses the impact of machine learning on fluid mechanics, emphasizing the importance of patterns in fluid flows and how machine learning algorithms like proper orthogonal decomposition can efficiently represent and extract these patterns, enabling the cleaning of noisy experimental data for higher fidelity flow estimates.', 'duration': 301.029, 'highlights': ['Proper Orthogonal Decomposition for Efficient Representation of Flow Patterns Proper orthogonal decomposition (POD) allows for the efficient representation of fluid flows as the sum of a few eigenflow fields or principal components, reducing the need for a million degrees of freedom to potentially only 10 POD modes, enabling powerful applications and leveraging algorithms from image processing.', 'Application of Modern Optimization Techniques to Clean Noisy Experimental Data By leveraging modern optimization techniques and robust statistics, an algorithm is able to decompose noisy experimental flow data into a true low rank component characterized by only a few POD modes, providing much higher fidelity flow estimates and cleaning up experimental measurements.', 'Impact of Machine Learning on Experimental Flow Measurements Machine learning, particularly through algorithms like proper orthogonal decomposition, can significantly enhance experimental flow measurements by cleaning up noisy experimental data and improving the fidelity of flow estimates, crucial for characterizing fluids in laboratory settings.', 'Utilizing Patterns in Data for Efficient Representation and Analysis The presence of low dimensional patterns in fluid flows allows for the application of algorithms directly from image processing, enabling the efficient representation and analysis of flow data and showcasing the potential of leveraging machine learning in fluid mechanics.', 'Significance of Patterns in Fluid Flows and Their Utilization in Machine Learning Research The existence of dominant patterns or coherent structures in complex fluid flows provides a major entry point for machine learning research, as the extraction, characterization, and utilization of these low dimensional patterns in big data, such as flow field data, are fundamental to machine learning applications in fluid mechanics.']}], 'duration': 396.148, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw591740.jpg', 'highlights': ['Proper Orthogonal Decomposition (POD) enables efficient representation of fluid flows, reducing degrees of freedom to potentially only 10 POD modes.', 'Leveraging modern optimization techniques and robust statistics, an algorithm decomposes noisy experimental flow data into a true low-rank component characterized by only a few POD modes.', 'Machine learning, particularly through algorithms like proper orthogonal decomposition, significantly enhances experimental flow measurements by cleaning up noisy experimental data and improving the fidelity of flow estimates.', 'The link between fluid mechanics and data-driven optimizations is a key aspect of research, indicating their intrinsic connection.', "Sir James Lighthill's criticism led to a cut in funding for artificial intelligence research in the 70s, known as the AI winter."]}, {'end': 1253.932, 'segs': [{'end': 1071.126, 'src': 'embed', 'start': 1039.335, 'weight': 0, 'content': [{'end': 1042.659, 'text': 'And this is common in all real-world turbulent fluids.', 'start': 1039.335, 'duration': 3.324}, {'end': 1048.827, 'text': 'So flow over a wing, or over a boat or a car, or in an engine over a windmill blade.', 'start': 1042.739, 'duration': 6.088}, {'end': 1055.075, 'text': "you're going to get this kind of turbulent, separated structures over this range of scales.", 'start': 1048.827, 'duration': 6.248}, {'end': 1057.897, 'text': 'But again, there are patterns that exist.', 'start': 1056.056, 'duration': 1.841}, {'end': 1064.101, 'text': 'There are large-scale structures that matter for drag and for lift and for mixing, for efficiency.', 'start': 1057.917, 'duration': 6.184}, {'end': 1071.126, 'text': 'And so we might not want to characterize every single degree of freedom in this extremely expensive simulation,', 'start': 1064.862, 'duration': 6.264}], 'summary': 'Real-world turbulent fluids exhibit large-scale structures affecting drag, lift, and efficiency in various applications.', 'duration': 31.791, 'max_score': 1039.335, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1039335.jpg'}, {'end': 1113.036, 'src': 'embed', 'start': 1086.217, 'weight': 5, 'content': [{'end': 1091.861, 'text': 'This is the Kolmogorov Turbulent Energy Cascade, which basically shows that if you have a turbulent flow,', 'start': 1086.217, 'duration': 5.644}, {'end': 1094.303, 'text': "you're going to have this massive scale separation.", 'start': 1091.861, 'duration': 2.442}, {'end': 1098.767, 'text': 'So the x-axis is basically spatial scales on a log plot.', 'start': 1094.764, 'duration': 4.003}, {'end': 1102.29, 'text': 'so big vertical structures are here on the left.', 'start': 1098.767, 'duration': 3.523}, {'end': 1105.012, 'text': 'little teeny, tiny vertical structures are here on the right.', 'start': 1102.29, 'duration': 2.722}, {'end': 1113.036, 'text': 'And real world fluids might have many, many, many orders of magnitude of scales, both in space and time.', 'start': 1105.692, 'duration': 7.344}], 'summary': 'Kolmogorov turbulent energy cascade demonstrates massive scale separation in turbulent flows with many orders of magnitude in space and time.', 'duration': 26.819, 'max_score': 1086.217, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1086217.jpg'}, {'end': 1173.588, 'src': 'embed', 'start': 1126.884, 'weight': 1, 'content': [{'end': 1133.589, 'text': 'Is it possible to approximate how these small scales affect the big energy-containing scales that we actually care about?', 'start': 1126.884, 'duration': 6.705}, {'end': 1139.233, 'text': 'Because these are often what we care about for lift and drag and things like that.', 'start': 1133.609, 'duration': 5.624}, {'end': 1142.896, 'text': 'And so this is a massive field called closure modeling.', 'start': 1139.894, 'duration': 3.002}, {'end': 1145.178, 'text': "And it's really, really important.", 'start': 1143.737, 'duration': 1.441}, {'end': 1148.28, 'text': "It's been a focus in fluids research for decades.", 'start': 1145.218, 'duration': 3.062}, {'end': 1154.965, 'text': "And there's this great review paper by Durasamy, Iaccarino, and Hsiao called Turbulence Modeling in the Age of Data.", 'start': 1149.301, 'duration': 5.664}, {'end': 1161.453, 'text': 'where they really dive into how machine learning and data-driven methods are being used to tackle this closure problem.', 'start': 1155.445, 'duration': 6.008}, {'end': 1171.485, 'text': 'And I think this is one of the most exciting areas where machine learning research can really make a practical impact on actual,', 'start': 1162.073, 'duration': 9.412}, {'end': 1173.588, 'text': 'everyday industrial flows.', 'start': 1171.485, 'duration': 2.103}], 'summary': 'Closure modeling in fluids research is important. machine learning and data-driven methods are being used to tackle the closure problem, as discussed in the review paper turbulence modeling in the age of data by durasamy, iaccarino, and hsiao.', 'duration': 46.704, 'max_score': 1126.884, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1126884.jpg'}, {'end': 1214.261, 'src': 'embed', 'start': 1191.983, 'weight': 4, 'content': [{'end': 1199.769, 'text': 'And so what Ling and colleagues did was, instead of just using a big deep neural network, which would be the most obvious kind of first thing,', 'start': 1191.983, 'duration': 7.786}, {'end': 1214.261, 'text': 'you might try what they did was design a custom deep neural network with these additional tensor input layers that essentially allowed them to encode or enforce prior physical knowledge about fluid flows.', 'start': 1199.769, 'duration': 14.492}], 'summary': 'Custom deep neural network with tensor input layers encodes prior knowledge about fluid flows.', 'duration': 22.278, 'max_score': 1191.983, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1191983.jpg'}], 'start': 989.692, 'title': 'Turbulent fluid dynamics and closure modeling with machine learning', 'summary': "Discusses patterns in turbulent fluids impacting drag, lift, and mixing, emphasizing the need for reduced order models. it also explores the significance of closure modeling using machine learning to approximate small scales' impact on big energy-containing scales, as outlined in the review paper 'turbulence modeling in the age of data' by durasamy, iaccarino, and hsiao.", 'chapters': [{'end': 1105.012, 'start': 989.692, 'title': 'Turbulent fluid dynamics', 'summary': 'Discusses the presence of patterns in turbulent fluids, such as the existence of large-scale structures that impact drag, lift, and mixing, and the need for reduced order models for computationally expensive simulations of turbulent boundary layers.', 'duration': 115.32, 'highlights': ['The presence of large-scale structures in turbulent fluids impacts drag, lift, and mixing, and requires reduced order models for computationally expensive simulations.', 'Turbulent flows exhibit massive scale separation, as depicted by the Kolmogorov Turbulent Energy Cascade, showing the range of spatial scales that exist in turbulent flows.', 'Simulations of turbulent boundary layers involve massive separation of scales, with intricate structures and details across a wide span of length scales and time scales.']}, {'end': 1253.932, 'start': 1105.692, 'title': 'Turbulence closure modeling with machine learning', 'summary': "Discusses the significance of closure modeling in fluid dynamics, where machine learning and data-driven methods are being used to approximate small scales' impact on big energy-containing scales, as highlighted in the review paper 'turbulence modeling in the age of data' by durasamy, iaccarino, and hsiao.", 'duration': 148.24, 'highlights': ['The importance of closure modeling in fluid dynamics and its focus on approximating how small scales affect big energy-containing scales for lift and drag. Closure modeling is significant for lift and drag in fluids research.', "The utilization of machine learning and data-driven methods in tackling the closure problem, as highlighted in the review paper 'Turbulence Modeling in the Age of Data' by Durasamy, Iaccarino, and Hsiao. Machine learning and data-driven methods are used in closure modeling, as discussed in the review paper by Durasamy, Iaccarino, and Hsiao.", 'The design of a custom deep neural network with additional tensor input layers to encode or enforce prior physical knowledge about fluid flows, as exemplified in the research by Ling and colleagues. Ling and colleagues designed a custom deep neural network with tensor input layers to incorporate physical knowledge about fluid flows.']}], 'duration': 264.24, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw989692.jpg', 'highlights': ['The presence of large-scale structures in turbulent fluids impacts drag, lift, and mixing, and requires reduced order models for computationally expensive simulations.', 'The importance of closure modeling in fluid dynamics and its focus on approximating how small scales affect big energy-containing scales for lift and drag.', "The utilization of machine learning and data-driven methods in tackling the closure problem, as highlighted in the review paper 'Turbulence Modeling in the Age of Data' by Durasamy, Iaccarino, and Hsiao.", 'Simulations of turbulent boundary layers involve massive separation of scales, with intricate structures and details across a wide span of length scales and time scales.', 'The design of a custom deep neural network with additional tensor input layers to encode or enforce prior physical knowledge about fluid flows, as exemplified in the research by Ling and colleagues.', 'Turbulent flows exhibit massive scale separation, as depicted by the Kolmogorov Turbulent Energy Cascade, showing the range of spatial scales that exist in turbulent flows.']}, {'end': 1806.865, 'segs': [{'end': 1285.113, 'src': 'embed', 'start': 1255.498, 'weight': 2, 'content': [{'end': 1262.301, 'text': 'So other areas that are really important super resolution is a technology that is really big in image sciences.', 'start': 1255.498, 'duration': 6.803}, {'end': 1266.583, 'text': 'And of course we can apply this directly to flow fields if we think about them as images.', 'start': 1262.842, 'duration': 3.741}, {'end': 1271.486, 'text': 'So this is data from the Johns Hopkins turbulence data set.', 'start': 1267.404, 'duration': 4.082}, {'end': 1277.709, 'text': 'And if you train on a large collection of images like these in a movie flow field images,', 'start': 1272.046, 'duration': 5.663}, {'end': 1285.113, 'text': 'then you can take very low-resolution or down-sampled versions of the flow field and reconstruct kind of this super-resolution,', 'start': 1278.309, 'duration': 6.804}], 'summary': 'Super resolution technology is crucial in image sciences and can be applied to flow fields, such as the johns hopkins turbulence data set, enabling reconstruction of low-resolution images.', 'duration': 29.615, 'max_score': 1255.498, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1255498.jpg'}, {'end': 1478.66, 'src': 'embed', 'start': 1451.446, 'weight': 3, 'content': [{'end': 1454.507, 'text': 'many hidden layers and nonlinear activation functions.', 'start': 1451.446, 'duration': 3.061}, {'end': 1461.01, 'text': 'So you can build these deep autoencoders that give you much, much better signal compression and reduction.', 'start': 1454.908, 'duration': 6.102}, {'end': 1465.412, 'text': 'So you would have the input be your high resolution flow image or flow field.', 'start': 1461.45, 'duration': 3.962}, {'end': 1472.456, 'text': 'And in the middle layer, these are kind of the latent variables or the dominant coherent structures.', 'start': 1466.312, 'duration': 6.144}, {'end': 1478.66, 'text': 'And then the decoder would use those few variables to reconstruct an estimate of the full flow field image.', 'start': 1472.897, 'duration': 5.763}], 'summary': 'Deep autoencoders offer superior signal compression, using latent variables to reconstruct flow field images.', 'duration': 27.214, 'max_score': 1451.446, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1451446.jpg'}, {'end': 1585.485, 'src': 'embed', 'start': 1557.948, 'weight': 4, 'content': [{'end': 1564.032, 'text': 'to enforce known physics and to get really accurate and efficient models of complex flow systems.', 'start': 1557.948, 'duration': 6.084}, {'end': 1565.933, 'text': 'Okay, good.', 'start': 1565.453, 'duration': 0.48}, {'end': 1569.635, 'text': 'So maybe kind of one of the last applications of this.', 'start': 1566.473, 'duration': 3.162}, {'end': 1575.398, 'text': "Once you have your models and you've extracted your patterns, one of the ultimate goals is to actually control your fluid.", 'start': 1569.715, 'duration': 5.683}, {'end': 1577.94, 'text': "You don't just want to understand it and model it.", 'start': 1575.418, 'duration': 2.522}, {'end': 1579.501, 'text': 'You want to manipulate your flow.', 'start': 1578.24, 'duration': 1.261}, {'end': 1581.842, 'text': 'So flow control is not this.', 'start': 1580.401, 'duration': 1.441}, {'end': 1585.485, 'text': 'This is what people think about a lot of times as kind of, again, magic.', 'start': 1581.882, 'duration': 3.603}], 'summary': 'Ultimate goal: to control fluid flow for accurate and efficient models.', 'duration': 27.537, 'max_score': 1557.948, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1557948.jpg'}, {'end': 1649.249, 'src': 'embed', 'start': 1623.371, 'weight': 0, 'content': [{'end': 1630.936, 'text': 'which basically shows that if you have a really really complicated flow system and you want to control it instead of using the full Navier-Stokes equations,', 'start': 1623.371, 'duration': 7.565}, {'end': 1638.802, 'text': 'which are far too expensive, what you can do is you can use machine learning to build these surrogate models that are fast and accurate,', 'start': 1630.936, 'duration': 7.866}, {'end': 1641.704, 'text': 'and fast enough to use in real time for feedback control.', 'start': 1638.802, 'duration': 2.902}, {'end': 1649.249, 'text': 'So this is a really nice diagram that you can use for lots of different types of machine learning models and lots of different types of control algorithms.', 'start': 1641.884, 'duration': 7.365}], 'summary': 'Using machine learning to build fast and accurate surrogate models for controlling complex flow systems in real time.', 'duration': 25.878, 'max_score': 1623.371, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1623371.jpg'}], 'start': 1255.498, 'title': 'Super-resolution and machine learning in fluid mechanics', 'summary': 'Discusses using super-resolution technology to reconstruct high-resolution flow field images and applying machine learning for controlling complex flow systems in fluid mechanics. it covers challenges, solutions, and real-time feedback control using large training databases and surrogate models.', 'chapters': [{'end': 1557.948, 'start': 1255.498, 'title': 'Super-resolution for flow field reconstruction', 'summary': 'Discusses the application of super-resolution technology to reconstruct high-resolution flow field images from low-resolution or down-sampled data, leveraging large training databases, with a focus on the challenges of interpolation and extrapolation tasks, the use of autoencoders for signal compression and reduction, and the development of reduced-order models for fluid dynamics.', 'duration': 302.45, 'highlights': ['The application of super-resolution technology to reconstruct high-resolution flow field images from low-resolution or down-sampled data. The technology involves training on a large collection of flow field images to reconstruct high-resolution images with all flow details, using a large offline training database to provide statistics of flow fields.', 'The challenges of interpolation and extrapolation tasks in super-resolution for flow fields. Interpolation tasks involve closely related data, while extrapolation tasks, such as predicting future weather patterns, are much more challenging and require additional physics to work effectively.', 'The use of autoencoders for signal compression and reduction in flow field analysis. Autoencoders can be used to decompose flow fields into dominant patterns, with the potential for deep autoencoders to provide better signal compression and reduction.', 'The development of reduced-order models for fluid dynamics using extracted patterns and data-driven methods. Patterns extracted through techniques like POD or autoencoders can be used to build efficient models for the evolution of modes in fluid dynamics purely from measurement data.']}, {'end': 1806.865, 'start': 1557.948, 'title': 'Machine learning for fluid control', 'summary': 'Discusses the application of machine learning in fluid mechanics, specifically in controlling complex flow systems, optimizing flow control objectives, and drawing inspiration from biology, with a focus on utilizing surrogate models for real-time feedback control.', 'duration': 248.917, 'highlights': ["Machine learning can be used to build surrogate models for controlling complex flow systems in real time. Using machine learning to build surrogate models allows for fast and accurate control of complex flow systems, as depicted in Katarina Beeker and Sebastian Peitz's diagram, enabling real-time feedback control.", 'Optimization problems in flow control can be increasingly well-solved with tools for machine learning. Utilizing machine learning tools can aid in solving optimization problems related to flow control objectives, such as increasing lift, decreasing drag, or enhancing mixing in a combustor, offering principled optimization of flow fields and control laws.', "Drawing inspiration from biology, particularly from the interactions of biological systems with complex flow fields, is a significant aspect of machine learning and fluid control research. The research is inspired by biology's proof of interaction with complex, turbulent flow fields, as seen in the elegant and adept maneuvers of eagles and insects, leading to the exploration of how biological systems make estimations and control decisions in flow environments."]}], 'duration': 551.367, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/8e3OT2K99Kw/pics/8e3OT2K99Kw1255498.jpg', 'highlights': ['Machine learning enables real-time feedback control of complex flow systems, improving accuracy and speed.', 'Utilizing machine learning tools aids in solving optimization problems related to flow control objectives.', 'Super-resolution technology reconstructs high-resolution flow field images from low-resolution data using large training databases.', 'Autoencoders can be used for signal compression and reduction in flow field analysis, potentially providing better compression with deep autoencoders.', 'Development of reduced-order models for fluid dynamics using extracted patterns and data-driven methods.']}], 'highlights': ["Machine learning's potential applications in physical sciences and engineering, particularly in fluid mechanics.", "Fluid mechanics' crucial role in trillion-dollar industries like health, defense, transportation, and energy.", 'Utilization of machine learning for fluid mechanics holds potential to enable advancements in energy and transportation systems.', 'Machine learning excels at building models from data using optimization, making it well-suited for fluid optimization problems.', 'Fluid optimization problems are nonlinear, nonconvex, multiscale, and very high dimensional.', 'The natural connection between machine learning and fluid optimization suggests direct application of machine learning techniques.', "The example of Newton's second law, F equals ma, is used to illustrate the ultimate interpretable and generalizable model, which covers a range of phenomena, even those not seen before.", 'Fluid dynamics generates tremendous amounts of data from theory, simulations, and experiments, making it a critical area for the integration of machine learning to solve optimization problems in modeling, control, and reduction.', 'The review paper from 2020 emphasizes the importance of robustness in machine learning for fluid mechanics, aiming for low-dimensional models that are robust to noise, disturbances, bad information, and new scenarios.', 'Proper Orthogonal Decomposition (POD) enables efficient representation of fluid flows, reducing degrees of freedom to potentially only 10 POD modes.', 'Leveraging modern optimization techniques and robust statistics, an algorithm decomposes noisy experimental flow data into a true low-rank component characterized by only a few POD modes.', 'Machine learning, particularly through algorithms like proper orthogonal decomposition, significantly enhances experimental flow measurements by cleaning up noisy experimental data and improving the fidelity of flow estimates.', 'The link between fluid mechanics and data-driven optimizations is a key aspect of research, indicating their intrinsic connection.', 'The presence of large-scale structures in turbulent fluids impacts drag, lift, and mixing, and requires reduced order models for computationally expensive simulations.', 'The importance of closure modeling in fluid dynamics and its focus on approximating how small scales affect big energy-containing scales for lift and drag.', "The utilization of machine learning and data-driven methods in tackling the closure problem, as highlighted in the review paper 'Turbulence Modeling in the Age of Data' by Durasamy, Iaccarino, and Hsiao.", 'Simulations of turbulent boundary layers involve massive separation of scales, with intricate structures and details across a wide span of length scales and time scales.', 'The design of a custom deep neural network with additional tensor input layers to encode or enforce prior physical knowledge about fluid flows, as exemplified in the research by Ling and colleagues.', 'Turbulent flows exhibit massive scale separation, as depicted by the Kolmogorov Turbulent Energy Cascade, showing the range of spatial scales that exist in turbulent flows.', 'Machine learning enables real-time feedback control of complex flow systems, improving accuracy and speed.', 'Utilizing machine learning tools aids in solving optimization problems related to flow control objectives.', 'Super-resolution technology reconstructs high-resolution flow field images from low-resolution data using large training databases.', 'Autoencoders can be used for signal compression and reduction in flow field analysis, potentially providing better compression with deep autoencoders.', 'Development of reduced-order models for fluid dynamics using extracted patterns and data-driven methods.']}