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.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
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: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.