Finite Element Method-enhanced Neural Network for Forward and Inverse Problems

图前向分布匹配用于分子逆设计

Graph Forward Distribution Matching for Molecular Inverse Design

GraphFDM通过前向过程优化图扩散模型，实现多属性分子逆设计，降低MAE达53%，化学有效性超0.99，并泛化到分布外属性组合。

基于学习的Kansa配点法用于超越线性的正向和反向PDEs

Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity

本文提出基于学习的Kansa配点法，用于解决超越线性的正向和反向PDEs问题，通过扩展CNF框架并应用到耦合和非线性场景，实现高效求解与自调技术。

Space-time shape uncertainties in the forward and inverse problem of electrocardiography

In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral for…

Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs

We propose quadratic residual networks (QRes) as a new type of parameter-efficient neural network architecture, by adding a quadratic residual term to the weighted sum of inputs before applying activation functions. With sufficiently high functional capacity (or expressive power), we show that it is especially powerful for solving forward and inverse physics problems involving partial differential equations (PDEs). Using tools from algebraic geometry, we theoretically demonstrate that, in contrast to plain neural networks, QRes shows better parameter efficiency in terms of network width and de…

评估AI增强的用于板几何中前向峰散射问题的单次扫描近似方法

Assessing AI-Enhanced Single-Sweep Approximations for Problems with Forward-Peaked Scattering in Slab Geometry

本文针对板几何中前向峰散射输运问题求解缓慢的挑战，评估了利用Fourier神经算子在预测-校正框架下获得AI增强的低阶、单次扫描输运方程解的可行性。

Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing PINNs are based on point-wise formulation with fully-connected networks to learn continuous functions, which suffer from poor scalability and hard boundary enforcement. Second, the infinite search space over-complicates the non-convex optimization for network training. Third, although the convolutional neural network (CNN)-based discrete learning can significant…