Volterra
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Related Articles from SNS
Reduced order modeling for spatio-temporal pattern approximation in diffusive Lotka-Volterra equations
arXiv:2606.04030v1 Announce Type: new Abstract: This paper presents an efficient reduced order modeling (ROM) framework for simulating spatio-temporal pattern formation in three-species diffusive Lotka-Volterra systems. To alleviate the high computational cost associated with long-time simulations of the high-dimensional full order model (FOM), we apply proper orthogonal decomposition (POD) to project the solution onto a low-dimensional subspace. Further efficiency is achieved through...
Revisiting Neural Processes via Fourier Transform and Volterra Series
arXiv:2606.01172v1 Announce Type: new Abstract: Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering. Neural processes (NPs), a family of probabilistic functional models, are promising solutions -- especially when endowed with domain-specific symmetries like translation equivariance, which improve sample efficiency and generalization. Yet existing translation-equivariant NPs face two limitations: (i) they...
High-Order Regularity and a Fully Discrete Fourier Spectral Method for a Partially Dissipative Viscoelastic Timoshenko System with Memory
arXiv:2606.09007v1 Announce Type: new Abstract: This paper investigates a class of partially dissipative viscoelastic Timoshenko systems with memory, where dissipation is induced by a Volterra-type memory term acting only on the shear variable. The well-posedness of weak and strong solutions is established on finite time intervals, including existence, uniqueness, stability, and higher-order regularity under compatibility conditions consistent with mixed boundary conditions. For the...
Cooperation, privatization and cheating in microbial exoenzyme synthesis: theoretical analysis in view of biotechnological applications
This study presents a mathematical framework for investigating the dynamics of coexistence and competition among heterotrophic microbes across different time scales. Focusing on metabolic interactions, we examine how three strategies: public metabolizing, private metabolizing, and cheating, shape population behaviour. The framework integrates generalized Lotka-Volterra dynamics with evolutionary game theory to capture the effects of resource exchange, particularly glucose made available by...
APIC: Amortized Physics-Informed Calibration using Neural Processes
Announce Type: new Abstract: Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems.
SkillSmith: Co-Evolving Skills and Tools for Self-Improving Agent Systems
Announce Type: new Abstract: Recent self-evolving agents have shown that skills can be discovered, refined, and accumulated through execution. However, existing skill-evolution frameworks typically assume a fixed tool layer and evaluate each skill independently, limiting their ability to repair tool-level failures or reason about interactions among skills.
A Multi-Invariant Preserving Discrete Gradient Methods
arXiv:2605.30827v1 Announce Type: new Abstract: This work introduces a novel structure-preserving methods for conservative systems based on a predictor-corrector strategy. The framework applies a discrete gradient correction to predictions generated by explicit one-step or multi-step schemes, which preserves nonlinear invariants while maintaining the accuracy order of the original predictor.
Coordinate-wise splitting algorithms for ODE simulation via Koopman-Lie product formulas
arXiv:2506.17524v3 Announce Type: replace Abstract: We present a computational framework for simulating finite-dimensional ordinary differential equations by combining classical Koopman-Lie product formulas with coordinate-wise frozen subflows. The setting is model-known, since the vector field is assumed to be available, and no data-driven approximation of the Koopman operator is attempted. Under standard assumptions, the Koopman-Lie generator associated with the flow admits a coordinate...