arXiv:2602. 05977v2 Announce Type: replace Abstract: We introduce Clifford Kolmogorov-Arnold Network (ClKAN), a flexible and efficient architecture for function approximation in arbitrary Clifford Algebra spaces.
arXiv:2604. 21174v3 Announce Type: replace-cross Abstract: Kolmogorov-Arnold Networks (KANs) replace fixed activations with learnable univariate edge functions whose behavior depends strongly on the chosen basis.
arXiv:2606. 02936v1 Announce Type: new Abstract: In this manuscript, we propose and analyze hierarchical Kolmogorov--Arnold neural network architectures employing radial basis functions as activation functions for approximating deterministic functions and random field models.
arXiv:2606. 22984v2 Announce Type: replace-cross Abstract: Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization.
arXiv:2209. 01432v4 Announce Type: replace-cross Abstract: In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\mathbb{R}^d$.
arXiv:2606. 09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics.
arXiv:2508. 11522v4 Announce Type: replace Abstract: Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks.
arXiv:2501. 17296v4 Announce Type: replace-cross Abstract: Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved computational efficiency they often fail to effectively capture intricate correlations inherent in coupled physical processes To address this limitation we introduce COMPOL a novel coupled multiphysics operator learning framework COMPOL extends conventional operator architectures by incorporating sophisticated recurrent and attentionbased aggregation mechanisms effectively modeling interdependencies among interacting physical processes within latent feature spaces Our approach is architectureagnostic and seamlessly integrates into various neural operator frameworks that involve latent space transformations Extensive experiments on diverse benchmarksincluding biological reactiondiffusion systems patternforming chemical reactions multiphase geological flows and thermohydromechanical processes demonstrate that COMPOL consistently achieves superior predictive accuracy compared to stateoftheart methods.
arXiv:2606. 20326v1 Announce Type: new Abstract: We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs).
arXiv:2607. 07127v1 Announce Type: cross Abstract: Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials.
arXiv:2602. 02056v3 Announce Type: replace-cross Abstract: Ultrafast online learning is essential for high-frequency systems, such as controls for quantum computing and nuclear fusion, where adaptation must occur on sub-microsecond timescales.
arXiv:2604. 15645v2 Announce Type: replace Abstract: We present QPINNACLE, an open-source computational framework for physics-informed neural networks (PINNs) that integrates modern training strategies, multi-GPU acceleration, and hybrid quantum-classical architectures within a unified modular workflow.
arXiv:2607. 02292v1 Announce Type: new Abstract: Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions.