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Research

Lorenz ODE Thesis

FYDP-II, defended: PINNs on the Lorenz-1960 system

PythonPyTorchSciPyPINNRK4 / DOP853pytest

Role

Thesis Researcher (Team Lead)

Duration

2025 - 2026

Date

2025 - 2026

Type

UIU Final Year Design Project

By the Numbers

118

Commits

41

Tests Defined

~3e-05

Reference Agreement

Immutable catalog

Archived Runs

Overview

My FYDP-II thesis code, public and evidence-first, now defended with the manuscript submitted to ICEEICT 2027. A physics-informed neural network solves the Lorenz-1960 system from the equations alone: the loss is the ODE residual, the reference solver runs only after training, and an 11,283-parameter network reaches within 3e-05 of a high-accuracy RK4/DOP853 baseline in under six minutes on a laptop CPU. Around the run of record sit a nine-architecture sweep and a windowed causal-weighting study for longer horizons. The repo preserves an immutable run catalog with settings hashes, per-collocation-point loss exports audited by hand, a two-branch source-code audit with repair notes, and provenance docs covering sixteen paper runs.

Tech Stack

PythonPyTorchSciPyPINNRK4 / DOP853pytest

Inside the Project

What it does, how it works, and what it ships.

science

The Question

Can a neural network solve a differential equation from the equations alone, without ever being shown the answer? The thesis answers with a residual-only PINN: a trial solution that satisfies the initial condition exactly, derivatives by autograd, and 3000 collocation points doing all the teaching.

fact_check

Training You Can Audit

The PINN's answer-key-free setup is provable: the loss is the ODE residual alone, the reference solver runs post-training, and per-collocation-point loss contributions are exported to CSV before each optimizer step. Historical runs are immutable, each with checkpoints, configs, and metrics.

  • Per-point loss CSV before every optimizer step
  • Immutable run catalog with settings hashes
  • Two-branch source-code audit and repair notes
  • Recovered trained models alongside the code
inventory_2

Companion Archive

  • A checksum-verified windowed-PINN archive (14-arm ablation)
  • verify_archive.py reloads all 16 models on a fixed 13,265-point reference grid
  • Adam + L-BFGS refinement with causal residual weighting

Outcomes

FYDP-II defended; manuscript submitted to ICEEICT 2027.

functions

~3e-05

Agreement vs DOP853

science

9+16

Sweep Runs + Windowed Models

article

Submitted

ICEEICT 2027 Manuscript

Interested in this project?

Reach out for source code walkthroughs or collaboration.