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Physics-Informed Neural ODEs for IBR Dynamics

Derivative and Trajectory Matching

C3-04 · Module outline

Compare noisy derivative labels with gradients through a numerical solver.

Learning objectives

  • Explain noise amplification during differentiation.
  • Trace reverse-mode gradients through an unrolled solver.

Concept outline

  1. Smoothing and finite-difference derivative estimates
  2. Trajectory losses and solver computation graphs
  3. Discrete adjoints and gradient checks

Experiment direction · Planned

Simulation and code experiment

Compare residual derivative matching with residual trajectory matching.

Model explanations, parameter settings, runnable code, and result interpretation will be developed here.

Practice and discussion

Check one directional gradient against a finite difference.

Worked solutions and feedback will accompany the full lesson.

Material preparation

Related notes, models, or notebooks are available and need adaptation into a web lesson and experiment.

Retain the transparent NumPy derivation and add an optional autodiff implementation.

All modules in this course
  1. Dynamical Systems and Trajectory Data
  2. Neural Network Foundations
  3. Neural ODEs and Learned Vector Fields
  4. Derivative and Trajectory Matching
  5. Physics Constraints and Residual Backbones
  6. Continuous-Time PINNs and Neural ODEs
  7. Parameter Identification and Generalization
  8. Stability Diagnostics for Learned Models
  9. From Swing Models to Converter Dynamics