arXiv AI
Automatic Differentiation with Constraints in Forward and Inverse Problems
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
Related stories
arXiv Machine Learning
Sep 15
Benchmarking Optimizers to Solve Inverse Problems with Differentiable Physics Simulators
arXiv:2609.13819v1 Announce Type: new Abstract: Solving inverse problems with differentiable physics simulators holds the potential to revolutionize scientific discovery and engineering design, as it...
arXiv AI
Jul 1
Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems
arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
arXiv Machine Learning
Jun 11
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.
arXiv Machine Learning
Jun 29
Mosaic: A Benchmark Suite for Differentiable Physics Solvers
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 Machine Learning
Sep 1
Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems
The paper introduces Sensitivity‑Constrained Neural Operators (SC‑NOs), which augment standard neural operator training with sampled Jacobian supervision from differentiable solvers or discrete adjoints. By matching selected sensitivities during training, SC‑NOs improve forward prediction accuracy and significantly enhance gradient‑based inverse reconstruction for distributed fields. Experiments on advection–diffusion, RANS–Spalart–Allmaras, high‑dimensional gridded inputs, and a shallow‑water tsunami source‑inversion case demonstrate that SC‑NOs achieve a better accuracy–cost trade‑off and enable near‑real‑time wave‑propagation forecasting from sparse observations.
arXiv Machine Learning
Jun 18
Acceleration of an algebraic multigrid pressure solver using graph neural networks
arXiv:2606. 19251v1 Announce Type: cross Abstract: Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularities.