rtqichen/torchdiffeq
Torchdiffeq
torchdiffeq este o bibliotecă PyTorch pentru rezolvarea ecuațiilor diferențiale ordinare (ODE), concepută pentru a rezolva probleme cu valori inițiale și pentru a construi framework-uri de tip neural ODE. Oferă un integrator ODE diferențiabil care permite modelelor de deep learning să simuleze profunzimea continuă prin integrarea funcțiilor dinamice în timp.
Biblioteca dispune de un calculator de gradient bazat pe metoda adjunctă pentru backpropagation eficient din punct de vedere al memoriei. Prin rezolvarea unui sistem adjunct augmentat înapoi în timp, calculează gradienții parametrilor fără a stoca fiecare stare intermediară a solver-ului.
Proiectul acoperă integrarea numerică cu solver-e adaptive și cu pas fix, încorporând controlul erorilor și interpolarea polinomială a stării. De asemenea, suportă gestionarea diferențiabilă a evenimentelor pentru a termina solver-ele atunci când funcții scalare specifice sunt declanșate și pentru a propaga gradienții prin timpul evenimentului.
Framework-ul este utilizat pentru aplicații precum fluxuri de normalizare continuă și transformarea distribuțiilor de probabilitate prin ecuații diferențiale ordinare învățate în timp continuu.
Features
- Memory-Efficient - Uses the adjoint method to compute gradients without storing every intermediate solver state.
- ODE-Based - Calculates gradients through ODE solvers using either direct backpropagation or the adjoint method.
- Adjoint Gradient Calculation - Performs memory-efficient backward passes using an adjoint solver to determine parameter gradients.
- Simulation Gradient Computations - Computes loss function gradients by solving an augmented adjoint system backwards in time to optimize memory.
- Neural Dynamics Models - Trains deep learning networks with continuous depth by integrating dynamics functions over a time interval.
- Neural ODE Frameworks - Provides a framework for building deep learning models that simulate continuous depth by integrating dynamics functions over time.
- Simulation Adjoint Kernels - Provides a memory-efficient adjoint method to compute gradients by solving a second differential equation backwards in time.
- Differentiable ODE Integrators - Computes system trajectories and propagates gradients through adaptive or fixed-step numerical solvers.
- Ordinary Differential Equation Solving - Computes solutions to initial value problems using adaptive or fixed-step ordinary differential equation solvers.
- Initial Value Problem Solvers - Computes the solution to initial value problems using adaptive or fixed-step solvers with configurable tolerances.
- Continuous-Depth Network Simulation - Integrates a dynamics function over a time interval to simulate a neural network containing an infinite number of layers.
- Differentiable Solver Termination - Supports terminating solvers exactly when specific scalar functions cross zero and propagates gradients through the event time.
- Differentiable Event Management - Provides a way to stop solvers based on event functions while propagating gradients through the stop time.
- Differentiable Event Simulation - Stops a differential equation solver when specific event functions trigger and propagates gradients through the event time.
- Event-Based Termination - Implements solver termination triggered by specific event functions with exact gradient computation at the stop time.
- Tensor Computation Graphs - Integrates with PyTorch's automatic differentiation engine to track operations and compute gradients across continuous-time dynamics.
- Integration Error Control - Adjusts adaptive solver step sizes using absolute and relative error tolerances to maintain numerical precision.
- Continuous-Time Density Transformations - Transforms simple probability distributions into complex densities by applying learned continuous-time ordinary differential equations.
- Continuous Normalizing Flows - Transforms simple distributions into complex densities by applying learned continuous-time ordinary differential equations.
- Adaptive-Step Integrators - Implements adaptive stepping to maintain numerical precision by adjusting intervals based on local error estimates.
- Computer Vision - Neural ordinary differential equations for continuous-depth models.
- Data Processing - Learning neural event functions for ordinary differential equations.
- Neural Differential Equations - Framework for neural ordinary differential equations.
- Data and Graph Processing - Solver for ordinary differential equations.
- Instrumente pentru dezvoltatori - Differentiable ODE solvers.
