Physics-Informed Neural Network

Scientific machine learning becomes useful when the learned model is constrained by governing physics and its assumptions remain inspectable.

The original project began as a transparent 1D heat-equation PINN. The next engineering problem was making the implementation reusable without copying the training loop for every new equation, while keeping domains, PDE residuals, boundary conditions, sampling, architectures, weighting, and optimization independently inspectable.

• Define domain and constraints
• Implement PDE residual
• Sample collocation / boundary points
• Select neural representation
• Construct weighted physics loss
• Train and diagnose
• Validate against reference

The generalized framework separates Domain, PDE, boundary conditions, sampling, neural representations, loss weighting, causal transient weighting, and GeneralTrainer components. New equations provide a residual implementation while reusing the surrounding infrastructure; the repository currently demonstrates 1D heat, 2D Poisson, and 1D Burgers problems alongside the original baseline and application-oriented examples.

• Generalized architecture supports arbitrary spatial dimensions with optional time dimensions.
• Dirichlet, Neumann, and periodic boundary-condition abstractions are separated from the PDE definition.
• Uniform, Latin Hypercube, Sobol, and residual-based adaptive sampling are available.
• Standard MLP, hard Dirichlet ansatz, Fourier features, fixed/gradient-norm/self-adaptive weighting, and causal weighting are implemented.
• Three generalized PDE problems are included: 1D heat, 2D Poisson, and nonlinear 1D Burgers.
• Recorded representative single-seed results include 9.96e-5 relative L2 for the hard-constraint Poisson configuration and 0.0052 max initial-condition error for the causal-weighted + L-BFGS Burgers configuration.
• Automated tests and CI cover the package across Python 3.10–3.12.

• Automated tests and CI cover the package across Python 3.10–3.12.
• Representative cases retain reference comparisons and recorded error measurements.

• Recorded measurements are single-configuration project results, not general PINN performance claims.
• The current framework is not an aerospace solver or safety-critical numerical method.
• Higher-dimensional aerospace validation requires stronger numerical baselines.

• Kept the original heat-equation baseline intact as a transparent learning and validation reference while building the generalized framework alongside it.
• Separated the PDE residual from the trainer so the same optimization infrastructure can be reused across equations.
• Added multiple sampling, boundary, network, and weighting strategies as interchangeable components rather than embedding them in individual examples.
• Documented representative measurements as project-specific single-seed results rather than presenting them as general claims about PINNs.
• Explicitly bounded the project as a research/engineering framework rather than a validated industrial or safety-critical solver.

Add matched multi-seed ablations, stronger error reporting, benchmark selected cases against classical numerical solvers, investigate training stability and weighting strategies, and extend toward higher-dimensional aerospace and fluid-mechanics problems with higher-fidelity references.

Explore all engineering work →