The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositions
Fuente:
arXiv
Saved in:
| Main Authors: | Heinlein, Alexander, Taraz, Johannes |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Learning on the Temporal Tangent Bundle for Physics-Informed Neural Networks
by: Jamal, Adetola, et al.
Published: (2026)
by: Jamal, Adetola, et al.
Published: (2026)
FieldTNN-based machine learning method for Maxwell eigenvalue problems
by: Jiang, Jiantao, et al.
Published: (2024)
by: Jiang, Jiantao, et al.
Published: (2024)
pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations
by: Kao, Tunan, et al.
Published: (2024)
by: Kao, Tunan, et al.
Published: (2024)
An adaptive Deep Ritz framework for second-order fully nonlinear partial differential equations
by: Caboussat, Alexandre, et al.
Published: (2026)
by: Caboussat, Alexandre, et al.
Published: (2026)
Deep operator network models for predicting post-burn contraction
by: Husanovic, Selma, et al.
Published: (2024)
by: Husanovic, Selma, et al.
Published: (2024)
Solving the BGK Model and Boltzmann equation by Fourier Neural Operator with conservative constraints
by: Hu, Boyun, et al.
Published: (2025)
by: Hu, Boyun, et al.
Published: (2025)
Expression Rates of Neural Operators for Linear Elliptic PDEs in Polytopes
by: Marcati, Carlo, et al.
Published: (2024)
by: Marcati, Carlo, et al.
Published: (2024)
Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
by: Codega, Gabriele, et al.
Published: (2025)
by: Codega, Gabriele, et al.
Published: (2025)
Approximation of Splines in Wasserstein Spaces
by: Justiniano, Jorge, et al.
Published: (2023)
by: Justiniano, Jorge, et al.
Published: (2023)
Physics-Informed Neural Networks: Bridging the Divide Between Conservative and Non-Conservative Equations
by: Neelan, Arun Govind, et al.
Published: (2025)
by: Neelan, Arun Govind, et al.
Published: (2025)
Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation
by: Wan, Jiayu, et al.
Published: (2025)
by: Wan, Jiayu, et al.
Published: (2025)
Physics-Informed Learning of Microvascular Flow Models using Graph Neural Networks
by: Botta, Paolo, et al.
Published: (2025)
by: Botta, Paolo, et al.
Published: (2025)
Operator Inference for Elliptic Eigenvalue Problems
by: Li, Haoqian, et al.
Published: (2025)
by: Li, Haoqian, et al.
Published: (2025)
Transport based particle methods for the Fokker-Planck-Landau equation
by: Ilin, Vasily, et al.
Published: (2024)
by: Ilin, Vasily, et al.
Published: (2024)
Enhancing PINN Accuracy for the RLW Equation: Adaptive and Conservative Approaches
by: Shehzad, Aamir
Published: (2025)
by: Shehzad, Aamir
Published: (2025)
Neural Discovery of Strichartz Extremizers
by: Valenzuela, Nicolás, et al.
Published: (2026)
by: Valenzuela, Nicolás, et al.
Published: (2026)
PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks
by: Visser, Coen, et al.
Published: (2024)
by: Visser, Coen, et al.
Published: (2024)
Convex Physics Informed Neural Networks for the Monge-Ampère Optimal Transport Problem
by: Caboussat, Alexandre, et al.
Published: (2025)
by: Caboussat, Alexandre, et al.
Published: (2025)
Solving Approximation Tasks with Greedy Deep Kernel Methods
by: Klink, Marian, et al.
Published: (2025)
by: Klink, Marian, et al.
Published: (2025)
Learning Neural Pushforward Samplers for Distributions from Fokker-Planck Equations by Weak Adversarial Training
by: He, Andrew Qing, et al.
Published: (2025)
by: He, Andrew Qing, et al.
Published: (2025)
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
by: Lorenz, Beatrice, et al.
Published: (2024)
by: Lorenz, Beatrice, et al.
Published: (2024)
Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations
by: Bai, Mengjia, et al.
Published: (2024)
by: Bai, Mengjia, et al.
Published: (2024)
Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems
by: Heinlein, Alexander, et al.
Published: (2024)
by: Heinlein, Alexander, et al.
Published: (2024)
A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling
by: Cui, Jianbo, et al.
Published: (2024)
by: Cui, Jianbo, et al.
Published: (2024)
ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions
by: Cai, Wei, et al.
Published: (2025)
by: Cai, Wei, et al.
Published: (2025)
The lowest-order Neural Approximated Virtual Element Method on polygonal elements
by: Berrone, Stefano, et al.
Published: (2024)
by: Berrone, Stefano, et al.
Published: (2024)
Quantitative Universal Approximation for Noisy Quantum Neural Networks
by: Gonon, Lukas, et al.
Published: (2026)
by: Gonon, Lukas, et al.
Published: (2026)
Weak Adversarial Neural Pushforward Method for the McKean-Vlasov / Mean-Field Fokker-Planck Equation
by: He, Andrew Qing, et al.
Published: (2026)
by: He, Andrew Qing, et al.
Published: (2026)
Discretization Error of Fourier Neural Operators
by: Lanthaler, Samuel, et al.
Published: (2024)
by: Lanthaler, Samuel, et al.
Published: (2024)
$\textit{A Priori}$ Error Analysis for the $p$-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
by: Kaltenbach, Alex, et al.
Published: (2025)
by: Kaltenbach, Alex, et al.
Published: (2025)
Tensor Neural Network Based Machine Learning Method for Elliptic Multiscale Problems
by: Lin, Zhongshuo, et al.
Published: (2024)
by: Lin, Zhongshuo, et al.
Published: (2024)
A posteriori certification for neural network approximations to PDEs
by: Ernst, Lewin, et al.
Published: (2025)
by: Ernst, Lewin, et al.
Published: (2025)
ConicCurv: A curvature estimation algorithm for planar polygons
by: Fuentes, R. Díaz, et al.
Published: (2025)
by: Fuentes, R. Díaz, et al.
Published: (2025)
Warped geometries of Segre-Veronese manifolds
by: Jacobsson, Simon, et al.
Published: (2024)
by: Jacobsson, Simon, et al.
Published: (2024)
Deep collocation method: A framework for solving PDEs using neural networks with error control
by: Weng, Mingxing, et al.
Published: (2025)
by: Weng, Mingxing, et al.
Published: (2025)
Space-time reduced basis methods for parametrized unsteady Stokes equations
by: Tenderini, Riccardo, et al.
Published: (2022)
by: Tenderini, Riccardo, et al.
Published: (2022)
Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows
by: Cao, Shuhao, et al.
Published: (2024)
by: Cao, Shuhao, et al.
Published: (2024)
Computing rough solutions of the KdV equation below ${\bf L^2}$
by: Cao, Jiachuan, et al.
Published: (2025)
by: Cao, Jiachuan, et al.
Published: (2025)
Latent Twins
by: Chung, Matthias, et al.
Published: (2025)
by: Chung, Matthias, et al.
Published: (2025)
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation
by: Schütte, Janina E., et al.
Published: (2024)
by: Schütte, Janina E., et al.
Published: (2024)
Similar Items
-
Learning on the Temporal Tangent Bundle for Physics-Informed Neural Networks
by: Jamal, Adetola, et al.
Published: (2026) -
FieldTNN-based machine learning method for Maxwell eigenvalue problems
by: Jiang, Jiantao, et al.
Published: (2024) -
pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations
by: Kao, Tunan, et al.
Published: (2024) -
An adaptive Deep Ritz framework for second-order fully nonlinear partial differential equations
by: Caboussat, Alexandre, et al.
Published: (2026) -
Deep operator network models for predicting post-burn contraction
by: Husanovic, Selma, et al.
Published: (2024)