Stabilizing PINNs: A regularization scheme for PINN training to avoid unstable fixed points of dynamical systems
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Abstract (arXiv)
It was recently shown that the loss function used for training physics-informed neural networks (PINNs) exhibits local minima at solutions corresponding to fixed points of dynamical systems. In the forward setting, where the PINN is trained to solve initial value problems, these local minima can interfere with training and potentially leading to physically incorrect solutions. Building on stability theory, this paper proposes a regularization scheme that penalizes solutions corresponding to unstable fixed points. Experimental results on four dynamical systems, including the Lotka-Volterra model and the van der Pol oscillator, show that our scheme helps avoiding physically incorrect solutions and substantially improves the training success rate of PINNs.
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References · 7
- 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 145
- 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 73
- 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 62
- 2022Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networkscited by 26
- 2022On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networkscited by 23
- 2022Improved Training of Physics-Informed Neural Networks with Model Ensemblescited by 19
- 2024Approximating Families of Sharp Solutions to Fisher's Equation with Physics-Informed Neural Networkscited by 5
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