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: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:2610.27888v1 Announce Type: new Abstract: Approximate solutions of partial differential equations (PDEs) on unstructured grids can be represented on a graph. Numerical optimization involving st...
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:2607. 07682v1 Announce Type: new Abstract: The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces.
arXiv:2602. 15648v2 Announce Type: replace Abstract: Inverse design problems are common in engineering and materials science.
The paper introduces Differentiable Diffusion Conditioning (D2C), an offline model‑based optimization approach that turns a frozen conditional diffusion model into a gradient‑based optimizer. By making the reverse denoising chain differentiable with respect to conditioning signals, D2C optimizes conditioning variables using gradients from surrogate objectives and physics‑informed penalties. The method is evaluated on laser pulse optimization for inertial confinement fusion, sustainable data‑center workload scheduling, and four Design‑Bench tasks, achieving top results on the real‑world tasks and the best average rank across the benchmarks.
arXiv:2406.04261v2 Announce Type: replace Abstract: Simulators are vital in science and engineering, as they faithfully model the influence of design parameters on real-world observations. Optimizing...
The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces.
The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.
The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.
arXiv:2610.04624v2 Announce Type: replace Abstract: Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for wh...