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Project Batch 1: Low-Fidelity Physics Informed Machine LearningðŸŠķ

âœĻ Interpretability is the primary focus! âœĻ

These projects emphasize interpretability over benchmark performance.

A successful experiment is therefore not defined solely by a low loss value, but by whether the resulting diagnostics support a coherent physical interpretation.

Project Batch Overview

Project 1 Overview

Project 1 investigates whether a neural network can recover physically meaningful trajectories by minimizing a variational physics residual rather than fitting data directly.

Key Idea

  • Enforce Euler-Lagrange structure through a soft constraint on the equation of motion.

Focus

  • forward modeling
  • variational loss functions
  • spectral bias and training stability
Project 2 Overview

Project 2 builds on this by asking what information remains identifiable in the context of a deliberately imperfect inverse problem.

Key Idea

  • Recover wavefunctions and potentials from noisy observations.

Focus

  • inverse operator learning
  • wavefunction reconstruction
  • identifiability of quantum states
  • normalization and stability constraints
Project 3 Overview

Project 3 reframes Hamiltonian learning as a self-consistent field problem.

Key Idea

  • The Hamiltonian is updated iteratively from its own induced quantum states, forming a fixed-point learning system.

Focus

  • SCF-style fixed-point iteration (inspired by DFT / PySCF)
  • Hamiltonian inference from noisy observables
  • weak symplectic regularization
  • POD-based structure discovery in learned state spaces

Unifying Theme

Across all three projects, the central question is:

How does physical structure emerge in neural systems when constraints are enforced only approximately rather than exactly?

Each project explores a different aspect of this question:

  • forward dynamics (Project 1)
  • inverse wavefunction reconstruction (Project 2)
  • self-consistent operator learning (Project 3)

Methodological Continuity

All projects share:

  • low-fidelity physics-informed neural networks
  • emphasis on interpretability over benchmark performance
  • small, exactly simulable systems
  • diagnostic-first evaluation philosophy

Long-Term Direction

This series serves as a foundation for exploring: - structure-preserving machine learning - inverse problems in quantum and classical systems - emergent geometry in learned physical systems

Project Batch 1 Github Repositories

🔗 Project 1

🔗 Project 2

Thank you for your patience!

Project 3 is still under development and project 1 and 2 artifacts are still being polished.