Physics-Informed Neural Network Surrogates with Polynomial Chaos-Based Uncertainty Propagation for Stochastic Model Predictive Control

arXiv:2609.23077 · eess.SY, cs.SY · Submitted 2026-09-19 · Read on arXiv

eess.SY, cs.SY

Submitted: 2026-09-19

Updated: 2026-09-19

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

Terminology

• Physics-Informed Neural Network — 9× in this paper
• Benchmark — 8× in this paper · explained in 2 episodes
• Uncertainty Quantification — 8× in this paper · explained in 8 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Polynomial Chaos Expansion — 7× in this paper
• Error Decomposition — 3× in this paper · explained in 3 episodes
• Inverse Problem — 3× in this paper · explained in 2 episodes
• Korteweg-de Vries — 3× in this paper
• Activation Function — 2× in this paper · explained in 1 episode
• Fidelity — 2× in this paper · explained in 2 episodes
• Loss Function — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• AdamW Optimizer — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Neural Network Approximation — 1× in this paper · explained in 2 episodes
• PDE residual — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Network (PINN) — 1× in this paper · explained in 3 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• A Single-Layer Asymmetric RNN: Potential Low Hardware Complexity Linear Equation Solver
• PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modeling

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