analiza aiqbench
This research introduces a fully differentiable graph-based implicit solver for partial differential equations, enabling efficient forward modeling and inverse problem solving through automatic differentiation with constraints. By integrating learnable graph coarsening, the method significantly reduces computational complexity while maintaining stability for stiff evolutionary and static problems in geophysics and engineering. The work bridges numerical analysis and machine learning to tackle large-scale optimization tasks where traditional solvers face scalability limits.
Automatic Differentiation with Constraints in Forward and Inverse Problems
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 stiff evolutionary and static PDEs often requires solving a large system of equations, which can be treated as a constraint. In this work, we present a fully differentiable graph-based implicit solver that incorporates this constraint. We evaluate its performance across four key tasks: a) linear and nonlinear forward modeling of evolutionary and static problems, b) solving inverse problems to estimate equation coefficients, c) solving inverse problems to estimate the right-hand side, and d) learnable graph coarsening to accelerate forward modeling. The stability and differentiability of our solver enable significant reductions in the complexity of forward modeling while efficiently addressing related inverse problems. These capabilities make it a powerful tool for different physics and engineering applications, in particular for geophysics, where inverse problems are commonly solved in order to reduce the model uncertainty.
Abstract:Approximate solutions of partial differential equations (PDEs) on unstructured grids can be represented on a graph. Numerical optimization involving stiff evolutionary and static PDEs often requires solving a large system of equations, which can be treated as a constraint. In this work, we present a fully differentiable graph-based implicit solver that incorporates this constraint. We evaluate its performance across four key tasks: a) linear and nonlinear forward modeling of evolutionary and static problems, b) solving inverse problems to estimate equation coefficients, c) solving inverse problems to estimate the right-hand side, and d) learnable graph coarsening to accelerate forward modeling. The stability and differentiability of our solver enable significant reductions in the complexity of forward modeling while efficiently addressing related inverse problems. These capabilities make it a powerful tool for different physics and engineering applications, in particular for geophysics, where inverse problems are commonly solved in order to reduce the model uncertainty.
Artificial Intelligence (cs.AI); Numerical Analysis (math.NA)
arXiv:2610.27888 [cs.AI]
(or arXiv:2610.27888v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.27888 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 248 cuvinte
Subiecte conexe
AcoustiPrint: Physics-Guided Neural Design of Manufacturable Acoustic Structures
arXiv · 23 oct. 2026
Real-Time and Accurate Collision-Free Teleoperation via Differentiable Constraint-Based Trajectory Planning
arXiv · 9 iun. 2026
DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers
arXiv · 4 aug. 2026
Cipher-Structure-Aware Variational Quantum Cryptanalysis: A Reversible Public-Diagnostic Framework
arXiv · 25 sept. 2026