Projected Neural Differential Equations for Learning Constrained Dynamics

arXiv:2410.23667 · cs.LG, physics.comp-ph, stat.ML · Submitted 2024-10-31 · Read on arXiv

cs.LG, physics.comp-ph, stat.ML

Submitted: 2024-10-31

Updated: 2026-09-08

Comments: 20 pages, 13 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Projected Neural Differential Equation — 8× in this paper
• Physical Constraints — 5× in this paper · explained in 7 episodes
• Conservation Laws — 4× in this paper · explained in 3 episodes
• Normalizing Flow — 4× in this paper · explained in 3 episodes
• Normalizing Flows — 4× in this paper · explained in 4 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Generalizability — 3× in this paper · explained in 6 episodes
• Riemannian optimization — 3× in this paper · explained in 2 episodes
• Chaotic Dynamics — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• North American Electric Reliability Corporation — 2× in this paper
• Stiefel manifold — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• AdamW Optimizer — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• DeepONet — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Meta-learning — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• Physics-Informed Deep Neural Operator Networks
• On Neural Differential Equations
• How to Avoid Trivial Solutions in Physics-Informed Neural Networks
• Universal Differential Equations for Scientific Machine Learning
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
• Machine Learning for Predicting Chaotic Systems
• ClimSim-Online: A Large Multi-scale Dataset and Framework for Hybrid ML-physics Climate Emulation

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