ADALib
ADALib is an Anti-Derivative Approximator (ADA)-based solver library for systems of ordinary differential equations (ODEs). It approximates derivative representations using orthogonal basis functions and reconstructs state trajectories through antiderivative integration.
Anti-Derivative Approximator (ADA)
Represents the derivative of each state using a compact set of trainable panel weights.
Reconstructs the state trajectory through antiderivative integration of the derivative representation.
Orthogonal basis representation
Approximates the derivative representation using orthogonal basis functions.
Provides a compact and structured representation of the solution over the time domain.
Hard enforcement of initial conditions
Initial conditions are naturally embedded through integration constants.
This allows the reconstructed trajectory to satisfy the prescribed initial condition without introducing a separate penalty term.
Physically interpretable panel weights
The panel-weight coefficients represent local derivative information over the solution domain.
Unlike opaque latent variables in black-box neural solvers, the trainable coefficients therefore carry an explicit physical meaning.
System-level ODE formulation
Users can directly define and train systems of coupled ODEs.
Complex neural-network architectures do not need to be implemented from scratch.
Physics-informed training
The trainable panel weights are optimized by minimizing the governing ODE residuals.
This enables solution of ODE systems without requiring paired reference-solution data.
Schematic illustration of anti derivative approximation:
Read the following paper for more information: “Anti-derivatives approximator for enhancing physics-informed neural networks”
Note
This project is under active development.