arXiv:2607. 23110v1 Announce Type: cross Abstract: In this paper, we study the extension of Neural Jump ODEs to infinite-dimensional function spaces.
arXiv:2603. 20467v2 Announce Type: replace-cross Abstract: Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties.
arXiv:2607. 14361v1 Announce Type: cross Abstract: We address fundamental challenges in representing and computing $\mathbb{R}^{d}$-valued predictable square-integrable processes over $[0,T]$, collected in the space $\mathcal{H}^2_T(\mathbb{R}^{d})$.
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
arXiv:2607. 19173v1 Announce Type: new Abstract: Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training.
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.
arXiv:2607. 00470v1 Announce Type: cross Abstract: We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time.
arXiv:2608. 14401v1 Announce Type: cross Abstract: In offline RL, estimating the optimal action-value function $Q^*$ can be formulated as solving the optimal Bellman equation based solely on offline observations.
arXiv:2606. 30384v1 Announce Type: new Abstract: Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape.
arXiv:2602. 15649v2 Announce Type: replace Abstract: In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series.
arXiv:2602. 16864v2 Announce Type: replace-cross Abstract: Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models.
arXiv:2605. 15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends.
Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape. However, the large number of trainable parameters makes the direct analysis of these dynamics challenging.