Spectral Representation Method

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3 papers in the last four weeks, down 57% on the four weeks before. 0.0% of all new papers.

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Neural networks for spectral optimization
Sep 28, 2026Alexis de Villeroché, Beniamin Bogosel, Stéphane Breuils +2Spectral Representation Method Neural Partial Differential Equation Solvers
Learning Conditional Expectation Operators via Functional Newton Updates
Sep 28, 2026Thiago Ramos, Alek Fröhlich, Daniel Perazzo +1Density Ratio Estimation Spectral Representation Method
Federal University of São Carlos · CSML, Istituto Italiano di Tecnologia and University of Genoa · CSML, Istituto Italiano di Tecnologia and University College London
Predicting Out-of-Distribution Generalization of Neural Operators via Observable Spectral Error Decomposition
Sep 20, 2026Hang-Cheng Dong, Pengcheng ChengNeural Operators Out-Of-Distribution
School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin 150001, China · School of Mathematics, Jilin University, Changchun 130012, China
EigenLI: Spectral Approximations to Late Interaction
Sep 7, 2026Archish S, Sabyasachi Basu, Ankit Garg +2Subspace Spectral Decomposition
Temple · Microsoft Research India
Spectral Convergence of Random Feature Method in Multiple Dimensions
Sep 3, 2026Pingbing Ming, Hao YuAtom-Averaged Features Spectral Representation Method
Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration
Aug 13, 2026Sabin Roman, Ljupco Todorovski, Saso DzeroskiSystem Identification Symbolic Regression
Department of Knowledge Technologies, Jožef Stefan Institute · Faculty of Mathematics and Physics, University of Ljubljana
Multi-kernel spectral clustering: Entrywise eigenvector perturbation bounds and exact recovery
Aug 9, 2026Zeqin Lin, Guangming Pan, Zhixiang Zhang +1Kernel Method Spectral Representation Method
1Nanyang Technological University · University of Macau · 3Dalian University of Technology
From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning
Aug 7, 2026Zhentao Tan, Ruijie Quan, Yi YangPartial Differential Equations Spectral Representation Method
Collaborative Innovation Center of Artificial Intelligence (CCAI), Zhejiang University, China
Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples
Aug 7, 2026Xinliang Liu, Tong Mao, Jinchao XuNeural Approximations Spectral Representation Method
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China · Shenzhen Loop Area Institute, Shenzhen 518000, P. R. China
Explicit and Stable Pseudospectral Time-Domain Method for the Föppl-von Kármán Equations
Aug 6, 2026Victor Zheleznov, Stefan BilbaoFinite Element Method Spectral Representation Method
Acoustics and Audio Group, University of Edinburgh, Edinburgh, UK · STMS (UMR9912), IRCAM, CNRS, Sorbonne Universit´e, Paris, France
Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models
Aug 5, 2026Liane Galanti, Devan Shah, Shlomo Fortgang +1System Identification Nonlinear Dynamics
Princeton University
Physics-informed reduced-order modelling with equivariant spectral submanifolds
Aug 4, 2026Georg MaierhoferReduced-Order Models Spectral Representation Method
Department of Applied Mathematics and Theoretical Physics · University of Cambridge, UK
Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation
Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural Approximations Partial Differential Equations
Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications
Jul 23, 2026Zhuan Liang, Zheng ZhaiSpectral Representation Method Community Detection
Department of Statistics, Faculty of Arts and Sciences at Beijing Normal University, Zhuhai
fSRD: Fuzzy Spectral Region Decomposition -- Automated Multi Operator Koopman Representations via an Adaptive Spectral Learning Architecture
Jul 20, 2026Charles Bokor, Mark Cary, Denise Morrey +1Koopman Operator Spectral Representation Method
School of Engineering, Computing and Mathematics Oxford Brookes University Oxford OX33 1HX, UK · Department of Aeronautical and Automotive Engineering Loughborough University Loughborough LE11 3TU, UK
Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs
Jul 15, 2026Tianchi Yu, Ivan OseledetsSpectral Representation Method Partial Differential Equations
1AXXX · 2Applied AI Institute · 3INM
Factorized Spectral Representations for Reinforcement Learning
Jul 15, 2026Junyi Wu, Dan LiSpectral Representation Method Transitions
Department of Industrial and Systems Engineering University of Washington Seattle, WA, USA
Near-Optimal Learning of Gaussian Sobolev Operators
Jul 8, 2026Ben Adcock, Michael Griebel, Gregor MaierProbabilistic Operator Learning Logarithmic Sobolev Inequalities
Department of Mathematics, Simon Fraser University, Burnaby BC, Canada · Institute for Numerical Simulation, University of Bonn, Bonn, Germany · Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Sankt Augustin, Germany
PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling
Jul 4, 2026Varvara Nazarenko, Timur Lidzhiev, Alexander TarakanovSpectral Representation Method Physics-Informed Learning
Faculty of Computer Science, HSE University, Moscow, Russia · AI VK, Moscow, Russia
From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
Jul 1, 2026Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan WaniorekFourier Neural Operators Nonlinear Operators
University of Chicago
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
Jun 27, 2026George Coote, Matthew J. ColbrookKoopman Operator Unsupervised Dictionary Learning
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, United Kingdom
Solve for the Hyperparameter, Skip the Search: Kolmogorov-Optimal Scaling Laws for Spline Regression
Jun 22, 2026Yong Yi Bay, Kathleen A. YearickKernel Ridge Regression General Grid Search Framework
PhD, University of Illinois at Urbana-Champaign
Measuring Model Robustness via Fisher Information: Spectral Bounds, Theoretical Guarantees, and Practical Algorithms
Jun 3, 2026Chong Zhang, Xiang Li, Jia Wang +2Robustness Verification Fisher Information Matrix
Xi’an Jiaotong-Liverpool University · The Chinese University of Hong Kong
Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
Jun 2, 2026Niccolò Perrone, Fanny Lehmann, Stefania Fresca +1Neural Operators Neural Partial Differential Equation Solvers
Université Paris-Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay · Laboratoire de Mécanique Paris-Saclay UMR 9026 · 8-10 rue Joliot Curie, 91190 Gif-sur-Yvette, France +5
Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent
Jun 1, 2026Ahanaf Hasan AriqSpectral Representation Method Gradient Descent
Ideal School and College
Data-Driven Spectral Prediction for Accelerating Large-Scale Electronic Structure Calculations
May 29, 2026Abhiram Badrinarayanan, Davor Davidovic, Edoardo Di Napoli +4Quantum Chemistry Density Functional Theory
Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany · CEA / IRIG / MEM / L_Sim, France
Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications
May 24, 2026Samuel B. Hopkins, Stefan TiegelSpectral Norm Approximation Algorithms
MIT
Geometric Dictionary Learning of Dynamical Systems with Optimal Transport
May 18, 2026Thibaut Germain, Sami Chemlal, Rémi Flamary +2Dynamical Systems Learning Dynamics
CMAP, Ecole Polytechnique · Istituto Italiano di Tecnologia & University of Novi Sad
Self-Distillation is Optimal Among Spectral Shrinkage Estimators in Spiked Covariance Models
May 18, 2026Radu Lecoiu, Debarghya Mukherjee, Pragya SurCovariance Self-Distillation Framework
Department of Statistics, Harvard University · Department of Mathematics & Statistics, Boston University
Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
May 14, 2026Arie Wortsman-Zurich, Hugo Tabanelli, Yatin Dandi +2Feature Learning Scaling Laws
Département d’Informatique, Ecole Normale Supérieure, PSL & CNRS · Information Learning and Physics Laboratory, École Polytechnique Fédérale de Lausanne (EPFL) · Statistical Physics of Computation Laboratory, École Polytechnique Fédérale de Lausanne (EPFL)
Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs
May 11, 2026Xuxiang Zhao, Angelica I. Aviles-RiveroNeural Operators Neural Partial Differential Equation Solvers
Qiuzhen College, Tsinghua University · YMSC, Tsinghua University
Bridging Spectral Operator Learning and U-Net Hierarchies: SpectraNet for Stable Autoregressive PDE Surrogates
May 9, 2026Enrique Hernández Noguera, Md Meftahul Ferdaus, Elias Ioup +2Neural Operators Partial Differential Equations
University of New Orleans, New Orleans, LA, USA · Naval Research Laboratory, Stennis Space Center, MS, USA
Orth-Dion: Eliminating Geometric Mismatch in Distributed Low-Rank Spectral Optimization
May 7, 2026Tatsuhiro Nakamori, Laura Gomezjurado Gonzalez, Ganesh Talluri +5Low-Rank Structure Spectral Representation Method
1Keio University · 2Stanford University · 3Midwestern University +3
Neural-Guided Domain Restriction to Accelerate Pseudospectra Computation for Structured Non-normal Banded Matrices
May 6, 2026Amit Punia, Rakesh Kumar, Madan LalSpectral Representation Method Matrix
1Jai Narain Vyas University, Jodhpur, Rajasthan, India · 2SRM University-AP, Amaravati, Andhra Pradesh, India · 3Jai Narain Vyas University, Jodhpur, Rajasthan, India
Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions
Apr 25, 2026Weihao Lu, Qian Lin, Yingcun Xia +1Kernel Ridge Regression Spectral Representation Method
Department of Statistics and Data Science, National University of Singapore. · Department of Statistics and Data Science, Tsinghua University.
SMART: A Spectral Transfer Approach to Multi-Task Learning
Apr 22, 2026Boxin Zhao, Mladen Kolar, Jinchi LvTransfer Learning Multi--Task Learning
University of Chicago · University of Southern California
Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
Apr 22, 2026Zhiheng Chen, Urban Fasel, Anastasia BizyaevaSystem Identification Spectral Representation Method
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA, 14850 · Department of Aeronautics, Imperial College London, London, United Kingdom
Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms
Apr 20, 2026Zhenhua Dang, Lei Zhang, Long Wang +1Coefficients System Identification
Optimal Centered Active Excitation in Linear System Identification
Apr 7, 2026Kaito Ito, Alexandre ProutiereSystem Identification Least Squares
Department of Information Physics and Computing, The University of Tokyo, Tokyo 113-8654, Japan · Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm 114 28, Sweden
Simplify to Amplify: Achieving Information-Theoretic Bounds with Fewer Steps in Spectral Community Detection
Feb 19, 2026Sie Hendrata Dharmawan, Peter ChinCommunity Detection Spectral Representation Method
Thayer School Of Engineering · Dartmouth College · Hanover, NH, USA
Learning to Discover Iterative Spectral Algorithms
Feb 10, 2026Zihang Liu, Oleg Balabanov, Yaoqing Yang +1Spectral Representation Method Self-Supervised Learning
1International Computer Science Institute · University of California, Berkeley · 4Lawrence Berkeley National Laboratory +1
Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation
Dec 9, 2025Muhammad Abid, Omer SanFourier Neural Operators Spectral Representation Method
Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville, TN 37996, USA.
A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
Sep 14, 2025Jia-Qi Yang, Lei ShiProbabilistic Operator Learning Nonlinear Operators
School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China.
Physics-Informed Support Vector Kernels via Green-Function Analogies and Jackson-Chebyshev Spectral Design
Feb 16, 2025Nan-Hong Kuo, Renata WongKernel Method Physics-Informed Learning
Department of Physics, National Taiwan University, Taipei, Taiwan · Department of Artificial Intelligence, Chang Gung University, Taoyuan, Taiwan · Department of Neurology, Chang Gung Memorial Hospital, Keelung, Taiwan +1
Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfer
Jan 18, 2025Haotian Lin, Matthew ReimherrMinimax Rate Kernel Ridge Regression
Department of Statistics, The Pennsylvania State University.
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
Jul 8, 2024Matthew J. Colbrook, Igor Mezić, Alexei StepanenkoKoopman Operator Spectral Representation Method
DAMTP, University of Cambridge, Cambridge, CB3 0WA, UK. · University of California, Santa Barbara, CA 93106, USA.

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Neural networks for spectral optimization

Alexis de Villeroché, Beniamin Bogosel, Stéphane Breuils, Dorin Bucur+1

Spectral Representation Method Neural Partial Differential Equation Solvers Spectral Neural Network Optimization Neural Network Landscapes

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Given a functional dependent on the spectrum of a differential operator, we address the problem of finding a domain which optimizes this functional. PDE solvers might be used to tackle this optimization. It is however computationally expensive. We propose two neural network models which learn the spectrum directly from the geometry of the domain and can be used to optimize the domain from one or more eigenvalues. We investigate two representations. The first encodes the domain through Fourier coefficients and a light MLP, which is efficient on star-shaped geometries, achieving a precision of 0.2%. Through a rescaling of the coefficients the designed models satisfy the scaling law of the eigenvalues. Additionally, averaging the outputs of the trained surrogates over rotations and reflections induces invariance for these transformations. The second is a model that takes the landscape function, the indicator function and the gradient of the landscape function. A Gram-Schmidt process produces orthogonal eigenfunctions as output of the model along with the associated eigenvalues. The landscape model reaches 1% mean relative error on the first ten eigenvalues, compared with 4% for an FNO model. Replacing the landscape by an SDF worsened both prediction and optimization errors. The trained model also generalizes from synthetic shapes to domains given as classical image dataset. The resulting surrogates of both approaches recover classical spectral optima such as the disk for the first eigenvalue or the conjectured minima of higher eigenvalues. This confirms that our models produce accurate differentiable estimates of eigenvalues, which can be used in shape optimization problems involving spectral quantities.

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