diffSPH - Differentiable Smoothed Particle Hydrodynamics for Adjoint Optimization and Machine Learning

diffSPH is a fully differentiable Smoothed Particle Hydrodynamics solver written in PyTorch with GPU acceleration. It is designed around differentiation from the ground up, so gradients propagate through the entire simulation rather than around it — which is what makes inverse problems, parameter estimation and learned closure models tractable.

Published in the Journal of Computational Physics (Winchenbach & Thuerey, 2026) and available on GitHub. A companion dataset, diffSPH16K, provides compressible and incompressible problems at a consistent 16K-particle resolution for training neural surrogates.

Schemes and features

Simulation schemes

δ-SPH and δ⁺-SPH for weakly compressible simulations
IISPH and DFSPH for incompressible simulations
CompSPH, CRKSPH, PESPH and the classic Monaghan scheme for compressible simulations

Boundary and domain handling

mDBC boundary conditions for rigid bodies
Inlets and outlets with buffer zones
Periodic BCs using minimum image conventions
Neumann and Dirichlet BCs

Numerics

grad-H, kernel renormalization and CRK correction schemes
δ⁺ and implicit particle shifting
Monaghan and Owen schemes for adaptive particle support radii
Balsara, Morris, Rosswog, and Cullen-Dehnen artificial viscosity switches
Sub-particle-scale turbulence modelling
Most common SPH kernel functions (Wendland, B-Spline, Poly6)

Infrastructure

Differentiable generation of initial conditions using SDFs
Hierarchical and compact hashing based neighbor searching
Verlet lists for neighborhood searches

What differentiability buys you

Because the solver is differentiable end to end, it supports inverse problems, loss-based physics, parameter estimation, shape optimization and closure modelling directly, rather than requiring a separate adjoint implementation to be written and maintained alongside the forward solver.

References

2026

diffSPH: Differentiable smoothed particle hydrodynamics for hybrid machine learning solutions in fluid mechanics

Rene Winchenbach, and Nils Thuerey

Journal of Computational Physics, 2026

Abs DOI arXiv Bib Code

We present diffSPH, a novel open-source differentiable Smoothed Particle Hydrodynamics (SPH) framework developed entirely in PyTorch with GPU acceleration. diffSPH is designed centrally around differentiation to facilitate optimization and machine learning (ML) applications in Computational Fluid Dynamics (CFD), including training neural networks and the development of hybrid models. Its differentiable SPH core, and schemes for compressible (with shock capturing and multi-phase flows), weakly compressible (with boundary handling and free- surface flows), and incompressible physics, enable a broad range of application areas. We demonstrate the framework’s unique capabilities through several applications, including addressing particle shifting via a novel, target- oriented approach by minimizing physical and regularization loss terms, a task often intractable in traditional solvers. Further examples include optimizing initial conditions and physical parameters to match target trajectories, shape optimization, implementing a solver-in-the-loop setup to emulate higher-order integration, and demonstrating gradient propagation through hundreds of full simulation steps. Prioritizing readability, usability, and extensibility, this work offers a foundational platform for the CFD community to develop and deploy novel neural networks and adjoint optimization applications.
@article{winchenbach2026diffsph, author = {Winchenbach, Rene and Thuerey, Nils}, title = {diffSPH: Differentiable smoothed particle hydrodynamics for hybrid machine learning solutions in fluid mechanics}, journal = {Journal of Computational Physics}, volume = {555}, pages = {114769}, year = {2026}, doi = {10.1016/j.jcp.2026.114769}, url = {https://doi.org/10.1016/j.jcp.2026.114769}, }