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Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…
Can linearly decodable failure signals in LLM hidden states be leveraged to correct those failures? We investigate this classification-correction gap via Overthinking (OT)--a stable behavioral regime (Jaccard >= 0.81, 94% inter-annotator…
Stepped-wedge cluster randomized trials (SW-CRTs) evaluate interventions rolled out across clusters over time. Standard analyses typically use immediate-treatment (IT) models, which assume effects begin at crossover and remain constant…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Routing configurations of a network should constantly adapt to traffic variations to achieve good network performance. Adaptive routing faces two main challenges: 1) how to accurately measure/estimate time-varying traffic matrices? 2) how…
Electronic health record (EHR) data are increasingly used to support real-world evidence (RWE) studies. Yet its ability to generate reliable RWE is limited by the lack of readily available precise information on the timing of clinical…
Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…
Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…
Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…
There has been a long history of using ordinary differential equations (ODEs) to understand the dynamics of discrete-time algorithms (DTAs). Surprisingly, there are still two fundamental and unanswered questions: (i) it is unclear how to…
Neural CDEs provide a natural way to process the temporal evolution of irregular time series. The number of function evaluations (NFE) is these systems' natural analog of depth (the number of layers in traditional neural networks). It is…
In this paper, we study the numerical discretization of stochastic differential equations with locally Lipschitz, super-linearly growing drift, and the resulting implications for sampling from non-log-concave distributions satisfying a…
Turbulent concentric coaxial pipe flows are numerically investigated as canonical problem addressing spanwise curvature effects on heat and momentum transfer that are encountered in various engineering applications. It is demonstrated that…
The Learning with Errors (LWE) problem underlies modern lattice-based cryptography and is assumed to be quantum hard. Recent results show that estimating entanglement entropy is as hard as LWE, creating tension with quantum gravity and…
In designing efficient feedback control laws for fluid flow, the modern control theory can serve as a powerful tool if the model can be represented by a linear ordinary differential equation (ODE). However, it is generally difficult to find…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…
Long-term time series forecasting (LTSF) is a challenging task that has been investigated in various domains such as finance investment, health care, traffic, and weather forecasting. In recent years, Linear-based LTSF models showed better…
Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…