A characterization of associative truncated products on polynomial spaces yields stochastic Galerkin fluxes that remain hyperbolic for the isothermal and compressible Euler equations in the tested regimes.
hub Canonical reference
arXiv preprint arXiv:2408.10205 , year=
Canonical reference. 100% of citing Pith papers cite this work as background.
22
Pith papers citing it
48
external citations · Pith
Background
100% of classified citations
abstract
A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.
hub tools
citation-role summary
background 5
citation-polarity summary
roles
background 5polarities
background 5representative citing papers
A Creator-Inspector multi-agent LLM pipeline for constitutive artificial neural networks increases the rate of models satisfying all nine physical constraints to 100% or 56% depending on the LLM backbone.
KAN-CL cuts catastrophic forgetting by 88-93% on Split-CIFAR-10/5T and Split-CIFAR-100/10T by anchoring KAN parameters at per-knot granularity while matching baseline accuracy.
In-context symbolic regression methods improve robustness of symbolic formula recovery from KANs, cutting median OFAT test MSE by up to 99.8 percent across hyperparameter sweeps.
QKAN is a quantum algorithmic framework using block-encodings and QSVT to implement wide-and-shallow networks for quantum learning and compositional state preparation.
DMK extended to rectangular cuboids with arbitrary periodicity via localized octree evaluations on cubical tilings and Fourier-space root-level summation with truncated kernels for reduced periodicity.
People navigate combinatorial risk by focusing on core features like post-investment success probabilities rather than computing the full induced distribution, unless the PMF is explicitly displayed.
beignet replaces random Fourier feature embeddings in PINNs with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy on PDE benchmarks with fewer parameters and near machine precision residuals on the inviscid Burgers blowup using Adam.
PU-GKAN applies Shepard normalization to Gaussian bases in KANs, yielding exact constant reproduction, reduced epsilon sensitivity, and better validation accuracy across tested regimes.
KLT-Net reconstructs the SN Ia distance modulus non-parametrically; with MFV M_B and flat-ΛCDM Bayesian/Hessian inference it yields H0 ≈ 69.6 km s⁻¹ Mpc⁻¹ and Ωm ≈ 0.30.
Lifting non-conservative, actuated, and contact-constrained robot dynamics into an exactly symplectic phase-space map yields state-of-the-art out-of-distribution autoregressive rollout error at low parameter and FLOP cost.
TPNet constructs multi-dimensional basis functions via tensor products of subnetwork outputs and solves for coefficients with least-squares to solve PDEs more efficiently than PINNs.
A hybrid KAN-MLP architecture with KAN input embedding and specialized LarctanKAN classification layer yields 5.33% average macro F1 gain over pure-MLP baselines in IMU-based human activity recognition.
Platform-independent formulas for KAN hardware inference complexity (RM, BOP, NABS) are derived for B-spline, GRBF, Chebyshev, and Fourier variants.
Overprovisioned KANs with sparsification, deep supervision, and depth selection under differentiable MDL yield smaller models with competitive accuracy on benchmarks.
Logistic KAN and KAAM achieve competitive or superior accuracy on clinical datasets compared to linear, tree, and neural baselines while providing built-in interpretability via symbolic forms and feature-wise decompositions.
Automated methods based on Deep Symbolic Regression and Kolmogorov-Arnold Networks discover compact, interpretable path loss models that achieve high accuracy and reduce prediction errors by up to 75% compared to traditional approaches on synthetic and real datasets.
KANLib is a unified, extensible KAN framework supporting adaptive grids and basis functions that reproduces reference performance on the California Housing benchmark with competitive speed.
KAN noise robustness in star/galaxy/quasar classification arises from implicit C2-spline regularization rather than architecture, as weight-decay-tuned MLPs match performance on SDSS and DESI data.
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
citing papers explorer
-
Hyperbolicity-Preserving Stochastic Galerkin Methods for Conservation Laws Based on Associative Truncated Products on Polynomial Spaces
A characterization of associative truncated products on polynomial spaces yields stochastic Galerkin fluxes that remain hyperbolic for the isothermal and compressible Euler equations in the tested regimes.
-
LLM-driven design of physics-constrained constitutive models: two agents are better than one
A Creator-Inspector multi-agent LLM pipeline for constitutive artificial neural networks increases the rate of models satisfying all nine physical constraints to 100% or 56% depending on the LLM backbone.
-
KAN-CL: Per-Knot Importance Regularization for Continual Learning with Kolmogorov-Arnold Networks
KAN-CL cuts catastrophic forgetting by 88-93% on Split-CIFAR-10/5T and Split-CIFAR-100/10T by anchoring KAN parameters at per-knot granularity while matching baseline accuracy.
-
In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks
In-context symbolic regression methods improve robustness of symbolic formula recovery from KANs, cutting median OFAT test MSE by up to 99.8 percent across hyperparameter sweeps.
-
QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation
QKAN is a quantum algorithmic framework using block-encodings and QSVT to implement wide-and-shallow networks for quantum learning and compositional state preparation.
-
Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework
DMK extended to rectangular cuboids with arbitrary periodicity via localized octree evaluations on cubical tilings and Fourier-space root-level summation with truncated kernels for reduced periodicity.
-
Decision-Making under Combinatorial Risk
People navigate combinatorial risk by focusing on core features like post-investment success probabilities rather than computing the full induced distribution, unless the PMF is explicitly displayed.
-
Fourier Feature Pyramids for Physics-Informed Neural Networks
beignet replaces random Fourier feature embeddings in PINNs with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy on PDE benchmarks with fewer parameters and near machine precision residuals on the inviscid Burgers blowup using Adam.
-
Partition-of-Unity Gaussian Kolmogorov-Arnold Networks
PU-GKAN applies Shepard normalization to Gaussian bases in KANs, yielding exact constant reproduction, reduced epsilon sensitivity, and better validation accuracy across tested regimes.
-
KAN-LSTM-Transformer Neural Networks, MFV and Cosmological Parameters
KLT-Net reconstructs the SN Ia distance modulus non-parametrically; with MFV M_B and flat-ΛCDM Bayesian/Hessian inference it yields H0 ≈ 69.6 km s⁻¹ Mpc⁻¹ and Ωm ≈ 0.30.
-
CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts
Lifting non-conservative, actuated, and contact-constrained robot dynamics into an exactly symplectic phase-space map yields state-of-the-art out-of-distribution autoregressive rollout error at low parameter and FLOP cost.
-
A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations
TPNet constructs multi-dimensional basis functions via tensor products of subnetwork outputs and solves for coefficients with least-squares to solve PDEs more efficiently than PINNs.
-
KAN-MLP-Mixer: A comprehensive investigation of the usage of Kolmogorov-Arnold Networks (KANs) for improving IMU-based Human Activity Recognition
A hybrid KAN-MLP architecture with KAN input embedding and specialized LarctanKAN classification layer yields 5.33% average macro F1 gain over pure-MLP baselines in IMU-based human activity recognition.
-
Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks
Platform-independent formulas for KAN hardware inference complexity (RM, BOP, NABS) are derived for B-spline, GRBF, Chebyshev, and Fourier variants.
-
Optimized Architectures for Kolmogorov-Arnold Networks
Overprovisioned KANs with sparsification, deep supervision, and depth selection under differentiable MDL yield smaller models with competitive accuracy on benchmarks.
-
Interpretable Clinical Classification with Kolmogorov-Arnold Networks
Logistic KAN and KAAM achieve competitive or superior accuracy on clinical datasets compared to linear, tree, and neural baselines while providing built-in interpretability via symbolic forms and feature-wise decompositions.
-
Automated Modeling Method for Pathloss Model Discovery
Automated methods based on Deep Symbolic Regression and Kolmogorov-Arnold Networks discover compact, interpretable path loss models that achieve high accuracy and reduce prediction errors by up to 75% compared to traditional approaches on synthetic and real datasets.
-
KANLib -- A Modular, Extensible and Fast Kolmogorov-Arnold Network Implementation
KANLib is a unified, extensible KAN framework supporting adaptive grids and basis functions that reproduces reference performance on the California Housing benchmark with competitive speed.
-
Kolmogorov--Arnold Networks as Implicit Regularizers: Noise Robustness and Interpretability for Stellar Classification
KAN noise robustness in star/galaxy/quasar classification arises from implicit C2-spline regularization rather than architecture, as weight-decay-tuned MLPs match performance on SDSS and DESI data.
-
A Practitioner's Guide to Kolmogorov-Arnold Networks
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
- Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate
- Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities