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A comprehensive survey reviewing recent advances in using artificial intelligence to solve inverse partial differential equation (PDE) problems, covering inverse problems, inverse design, and control problems, with applications across scientific and industrial domains.
This paper introduces breakeven complexity, a metric to determine when neural PDE solvers become cost-effective compared to traditional numerical solvers. The framework uses scaling laws to allocate training budgets and evaluates multiple neural solvers on diverse PDE benchmarks.
Tadpole introduces a foundation model for 3D PDEs, pre-trained as an autoencoder via efficient online data generation, enabling large-scale diverse training without storage overhead. It demonstrates strong fine-tuning performance for dynamics learning and generative modeling across heterogeneous physical systems.
Introduces UFO, a cross-domain neural operator framework that adaptively learns operators across different representational domains, enabling discretization-decoupled predictions robust to distribution shifts.
This paper proposes a topology-preserving neural operator learning method using Hodge decomposition to separate topological and geometric components, improving accuracy and efficiency on geometric meshes.
This paper introduces Geometric Kolmogorov-Arnold Networks (GeoKAN), a family of geometry-aware models that learn Riemannian metrics to adapt coordinates for improved function approximation and physics-informed learning.
This paper proposes a new architecture that augments Flux Neural Operators with recurrent Vision Transformers to solve conservation laws as a foundation model. It demonstrates robust generalization and long-time prediction capabilities across diverse conservative systems without explicit access to governing equations.
This paper proposes a self-supervised physics-informed neural network (PINN) framework with a learnable blending neuron to adaptively balance physics-based and data-driven losses, and integrates transfer learning to improve efficiency under data scarcity. It is validated on liquid-metal miniature heat sink CFD data with only 87 datapoints, achieving under 8% error.