arXiv Machine Learning
Jun 4
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
Low-Rank Kolmogorov-Arnold Generator Flows for Interpretable Operator Learning
The paper introduces KAFlow, a low‑rank Kolmogorov‑Arnold flow that learns the generator of physical operators as a compact symbol composed of univariate Kolmogorov‑Arnold functions. By fixing the gauge of these functions, integrating dynamics with exact exponential integrators, and automatically distilling closed‑form expressions, KAFlow achieves markedly lower out‑of‑distribution loss and higher precision on synthetic benchmarks, long‑horizon quantum dynamics, and variable‑order fractional operators. The method recovers operator coefficients to within 10⁻⁴ and discovers complex dispersion relations that sparse regression cannot capture.
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arXiv Machine Learning
Jul 27
Explainable quantum-compressed machine learning for complex fluid flows
arXiv:2607. 21688v1 Announce Type: cross Abstract: Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box.
arXiv Machine Learning
Jun 5
On the training of physics-informed neural operators for solving parametric partial differential equations
arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.
arXiv Machine Learning
Oct 8
Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows
The paper introduces a kernel‑based operator learning method that preserves key physical properties—such as incompressibility, periodicity, and turbulence—of the incompressible Navier–Stokes equations. By mapping input functions to expansion coefficients in a property‑preserving kernel basis, the method guarantees that predicted velocity fields analytically maintain these properties. The authors provide theoretical convergence guarantees, develop efficient computational techniques for large‑scale training, and demonstrate significant accuracy and speed improvements over neural operators on 2D and 3D flow benchmarks.
arXiv Machine Learning
Aug 26
Physics-Integrated Operator Learning via Gaussian Splatting Representations
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
arXiv Machine Learning
Aug 14
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv Machine Learning
Jul 22
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv Machine Learning
Jun 9
GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators
arXiv:2606. 08343v1 Announce Type: new Abstract: We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space.
arXiv Machine Learning
6d ago
Fractional is Better: Learnable Derivative Orders in Neural Operator Learning
arXiv:2610.20363v1 Announce Type: new Abstract: Neural operators learn mappings between function spaces, enabling fast surrogate solutions to partial differential equations. Despite remarkable archit...
arXiv Machine Learning
Sep 30
SINO: Scale-Invariant Neural Operator
arXiv:2609.36890v1 Announce Type: new Abstract: In scientific machine learning, physical fields governed by partial differential equations exhibit low-rank structure and scale invariance. When solvin...
arXiv Machine Learning
Jul 3
An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
arXiv Machine Learning
Jun 3
Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.