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We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…
We consider the problem of spatiotemporal sampling in which an initial state $f$ of an evolution process $f_t=A_tf$ is to be recovered from a combined set of coarse samples from varying time levels $\{t_1,\dots,t_N\}$. This new way of…
Network science has become an essential interdisciplinary tool for understanding complex biological systems. However, because these systems undergo continuous, often stimulus-driven changes in both structure and function, traditional static…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
Developing agents that can perform complex control tasks from high dimensional observations such as pixels is challenging due to difficulties in learning dynamics efficiently. In this work, we propose to learn forward and inverse dynamics…
We present time-constrained automata (TCA), a model for hard real-time computation in which agents behaviors are modeled by automata and constrained by time intervals. TCA actions can have multiple start time and deadlines, can be…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
The steady-state approximation (hereafter abbreviated as SSA) consists in setting $dy/dt=0$, where $y$ denotes the concentration of a short-lived intermediate subject to first-order decay with a rate constant $k$. The sole reason for…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability…
Test Time Adaptation (TTA) is a pivotal concept in machine learning, enabling models to perform well in real-world scenarios, where test data distribution differs from training. In this work, we propose a novel approach called pseudo Source…
This paper investigates test-time adaptation (TTA) for regression, where a regression model pre-trained in a source domain is adapted to an unknown target distribution with unlabeled target data. Although regression is one of the…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by…
Active matter systems provide fascinating examples of pattern formation and collective motility without counterparts in equilibrium systems. Here, we employ Brownian dynamics simulations to study the collective motion and self-organization…
This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…
The second law of thermodynamics states that entropy production in macroscopic systems is non-negative, reaching zero only at thermodynamic equilibrium. As a corollary, this implies that the state trajectory of macroscopic systems is…
Domain generalization aim to train models to effectively perform on samples that are unseen and outside of the distribution. Adversarial data augmentation (ADA) is a widely used technique in domain generalization. It enhances the model…