Differentiable simulation is a key component in learning, control, and inverse problems, where gradients through nonlinear implicit solvers are required. Existing approaches either rely on unrolled automatic differentiation, whose memory grows with solver depth, or on equation-level implicit differentiation, which assembles global Jacobians and solves large sparse adjoint systems, discarding the locality of the forward solver -- and differentiating the converged equation rather than the finite computation that actually ran.
arXiv:2608. 08559v1 Announce Type: cross Abstract: Differentiable simulation is a key component in learning, control, and inverse problems, where gradients through nonlinear implicit solvers are required.
arXiv:2609.08800v1 Announce Type: cross Abstract: Three properties determine whether a differentiable simulator can drive gradient-based optimization through contact: simulation accuracy, gradient re...
GRADSOLVE is an open‑source JAX library that provides fast, exact reverse‑mode gradients for low‑dimensional ordinary differential equation (ODE) ensembles on NVIDIA GPUs. It records the accepted steps of an adaptive solver and differentiates a fixed‑step replay, yielding the exact discrete adjoint at a lower computational cost than traditional checkpointed methods. Benchmarks show that GRADSOLVE’s forward kernel is 2.8× faster than DiffEqGPU.jl, and its gradient computation is 5.6–14.1× faster than Diffrax’s checkpointed adjoint while maintaining matched forward‑state accuracy across multiple GPU generations.
arXiv:2606. 27895v1 Announce Type: cross Abstract: Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented.
arXiv:2607. 01128v1 Announce Type: new Abstract: Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation.
arXiv:2608. 08608v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate.
arXiv:2607. 18020v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
arXiv:2607. 18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
The paper presents a reinforcement‑learning framework that dynamically selects between full‑order models (FOMs) and reduced‑order models (ROMs) in hybrid domain decomposition simulations using the overlapping Schwarz alternating method (O‑SAM). Offline‑trained Deep Q‑networks choose subdomain‑local FOMs or pre‑trained Operator Inference ROMs based on a reward that balances accuracy, computational cost, and model‑switching frequency, and the learned policies are deployed on unseen problem instances without needing a reference FOM solution. Experiments on a 1D advection‑diffusion problem and a 3D elastic wave propagation benchmark show that the RL‑guided policies adaptively allocate high‑fidelity resolution as features propagate, outperforming static FOM/ROM assignments and demonstrating the feasibility of predictive online fidelity adaptation in Schwarz‑based hybrid simulations.
arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.
arXiv:2602. 06219v2 Announce Type: replace-cross Abstract: World models offer a promising avenue for more faithfully capturing complex dynamics, including contacts and non-rigidity, as well as complex sensory information, such as visual perception, in situations where standard simulators struggle.
arXiv:2606. 24039v1 Announce Type: cross Abstract: Robotics increasingly relies on GPUs for parallel simulation, large-scale learning, and neural-network inference.