arXiv:2607. 05280v1 Announce Type: new Abstract: Many real-world systems evolve continuously, yet most machine learning models interpret time series as discrete sequences.
arXiv:2601. 13534v3 Announce Type: replace-cross Abstract: Time series generation (TSG) is widely used across domains, yet most existing methods assume regular sampling and fixed output resolutions.
arXiv:2606. 19138v1 Announce Type: new Abstract: Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori.
The paper proposes a new interpretable machine learning approach for discovering unknown nonlinear ordinary differential equations from a single state trajectory. It differs from existing methods by deriving its formulation from Functional Analysis and Operator Theory and by defining a cost function as an integral distance between functions rather than a discrete error sum. An incremental learning algorithm enables online updates, allowing simultaneous identification of both system dynamics and external time‑varying forces, with numerical examples illustrating its benefits.
arXiv:2601. 20361v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time.
The paper surveys continuous‑time (CT) machine learning, a framework for modeling temporal dynamics as continuous processes, especially useful when data are sampled irregularly or over long horizons. It introduces a unified taxonomy that groups major CT methods by their underlying mathematical formulations and shows how different architectural choices—such as vector‑field parameterization, stochasticity, memory mechanisms, and discretization—relate these families. The survey compares training algorithms, optimization strategies, failure modes, computational complexity, and benchmarks, reviews supporting software ecosystems, and outlines open challenges and future research directions.
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.
arXiv:2608.22112v1 Announce Type: cross Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...
arXiv:2605. 25413v3 Announce Type: replace-cross Abstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs).
arXiv:2608.30328v1 Announce Type: new Abstract: Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditio...
Continuous-time (CT) machine learning has emerged as a principled framework for modeling temporal dynamics as a continuous process, particularly when observations are sampled at arbitrary time points...
arXiv:2509.06154v3 Announce Type: replace Abstract: Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings bet...
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).