Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
summary
Combines Gaussian-process surrogates and physics-informed priors to learn nonlinear PDEs and parameters from tiny datasets: design optimization of a hydrofoil finds the maximum with about 13 high-fidelity runs plus many 6-minute low-fidelity solves; physics-informed GPs turn PDE coefficients into kernel hyperparameters so two noisy snapshots can identify Burgers or Reynolds numbers; physics-informed neural nets (e.g. 10-layer, 256-neuron tanh network) recover velocity and pressure from passive-scalar data, scale to 100-D Black–Scholes, but fail when the modeled equations omit real experimental forces like gravity.
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chapters (13)
- 0:00Introduction by Maziar Raissi
- 1:06Speaker introduction and background
- 13:03Gaussian processes for design optimization
- 19:23Physics-informed Gaussian processes
- 25:07Solving forward and inverse problems
- 31:17Scaling Gaussian processes for big data
- 35:38Neural networks for scientific computing
- 40:22Physics-informed neural networks
- 48:23High-dimensional PDEs with neural networks
- 51:37Learning parameters and new dynamics
- 56:23Pressure field reconstruction in aneurysms
- 1:01:19Applications and future directions
- 1:05:17Q&A session
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