torchsde and torchcde
These two tools are complements, as `torchsde` provides differentiable stochastic differential equation (SDE) solvers while `torchcde` offers differentiable controlled differential equation (CDE) solvers, addressing different mathematical formalisms that can arise in the "neural-differential-equations" domain and potentially be used in conjunction for more complex systems.
About torchsde
google-research/torchsde
Differentiable SDE solvers with GPU support and efficient sensitivity analysis.
Implements multiple SDE solver algorithms (Euler, Milstein, adaptive-step) with configurable noise types (scalar, diagonal, general) and supports both Itô and Stratonovich calculus. Enables end-to-end learning of latent SDEs and neural SDE-based generative models through PyTorch autograd, with adjoint-based sensitivity analysis for memory-efficient backpropagation. Integrates seamlessly with PyTorch's `nn.Module` API and demonstrated on applications including VAE-style latent dynamics and adversarial SDE training.
About torchcde
patrick-kidger/torchcde
Differentiable controlled differential equation solvers for PyTorch with GPU support and memory-efficient adjoint backpropagation.
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