FDS Talk: Sifan Wang (UPenn),”Physics-informed machine learning: Theory, Algorithms, and Applications”

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Webcast

NOTE: This talk will be virtual only by Zoom.
Click the button below or go to: https://yale.zoom.us/j/97109392635

Abstract: The remarkable potential of deep learning in areas from computer vision to natural language processing has now found profound implications in modeling and simulating physical systems. Central to these advancements is the emerging field of physics-informed machine learning (PIML), a fusion of physical principles with machine learning frameworks. Our study delves into the inherent challenges and limitations of PIML, particularly in the physics-informed neural networks (PINNs) and deep operator networks (DeepONets). Firstly, we investigate the gradient flow of PINNs, identifying a training failure stemming from unbalanced back-propagated gradients. This insight motivates us to generalize the Neural Tangent Kernel (NTK) theory to PINNs. With this tool, we theoretically reveal that the training of PINNs suffer from spectral bias, causality violation and discrepancy in convergence rate of loss term. To address these critical issues, we propose several simple yet effective training algorithms and network architectures, and validate them across a wide range of representative benchmarks in computational physics.

Moreover, we highlight the data-intensive demands of training neural operators and the potential inconsistency of their predictions with the underlying physics. To resolve these challenges, we propose physics-informed DeepONet, introducing a simple and effective regularization mechanism for biasing the outputs of DeepONet models towards ensuring physical consistency. Based on that, we propose a autoreressive training algorithm for performing long-time integration of evolution equations in a self-supervised manner. Furthermore, we leverage the proposed framework to build fast and differentiable surrogates for rapidly solving PDE-constrained optimization problems, even in the absence of any paired input-output training data. In summary, we provide in-depth exploration into theory, algorithms and applications aspects of physics-informed machine learning, providing new insights into developing scientific machine learning with better robustness and accuracy guarantees, as needed for many critical applications in computational science and engineering.

NOTE: This talk will be virtual only by Zoom.
Click the box above or go to the following link: https://yale.zoom.us/j/97109392635


Sifan Wang (UPenn)

Speaker Bio: I am Ph.D student in Applied Math and Computational Science at the University of Pennsylvania. My research interests lie in the emerging area of physics-informed machine learning with an emphasis on physics-informed neural networks and DeepONets.

Website: https://www.linkedin.com/in/sifan-wang-0792a5223/