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.
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:2607. 24777v1 Announce Type: new Abstract: Architected metamaterials derive their functions from structure, creating vast opportunities to program physical responses through topology design.
KATOsuper is an objective‑agnostic framework that accelerates neural topology optimization by coupling neural‑reparameterized TO with a Sensitivity‑Consistent Fourier Neural Operator (SC‑FNO). It uses a forward_split architecture to ensure that sensitivities derived via automatic differentiation remain consistent with predicted objectives, enabling stable optimization. The method demonstrates significant deployment‑time speedups (15–110×) over MATLAB baselines while preserving optimality across 2D and 3D benchmark problems, including compliance and stress minimization, and supports zero‑shot extrapolation to higher resolutions.
arXiv:2602. 15648v2 Announce Type: replace Abstract: Inverse design problems are common in engineering and materials science.
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...
Co-PiLOT is a latent optimization framework that maps candidate physical structures through a generative encoder-decoder, using the decoder as a learned validity prior and performing physics-informed black-box optimization in latent space. It is applied to the inverse design of magnesium alloy microstructure/texture, employing a vision transformer encoder paired with latent diffusion, diffusion transformer, and rectified-flow transformer decoders trained on an 80,000-sample EBSD dataset to produce a minimal bottleneck representation. The MERIDIAN optimizer, driven by a deep-kernel Gaussian process and failure-aware feasibility prediction, achieves the best target-driven objective score within 160 simulations, reducing relative target error by 3–22% compared to seven baseline methods.
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: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. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
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:2607. 24274v1 Announce Type: cross Abstract: Inverse design of three-dimensional porous media is central to applications in filtration, catalysis, energy storage, fuel cells, thermal management, and biomedical scaffolds, but remains challenging because many distinct pore geometries can share similar porosity or permeability while small structural changes can strongly affect transport behaviour.
arXiv:2606. 20442v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training.