Related papers: A unified framework for data-driven construction o…
Modeling car-following behavior is fundamental to microscopic traffic simulation, yet traditional deterministic models often fail to capture the full extent of variability and unpredictability in human driving. While many modern approaches…
Non-Markovian dynamics are ubiquitous across physics, biology, and engineering. Yet our understanding of non-Markovian processes significantly lags that of simpler Markovian processes, due largely to a lack of tractable models. In this…
Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…
Studies of the dynamics of a quantum system coupled to baths are typically performed by utilizing the Nakajima-Zwanzig memory kernel (${\mathcal{K}}$) or the influence functions ($\mathbf{{I}}$), especially when the dynamics exhibit memory…
We present a variational principle for the extraction of a time-dependent orthonormal basis from random realizations of transient systems. The optimality condition of the variational principle leads to a closed-form evolution equation for…
This study presents a novel physics informed, data-driven modeling framework for capturing the strongly nonlinear thermo-viscoelastic behavior of soft materials exhibiting stress softening, with emphasis on the Mullins effect. Unlike…
In "Large Associative Memory Problem in Neurobiology and Machine Learning," Dmitry Krotov and John Hopfield introduced a general technique for the systematic construction of neural ordinary differential equations with non-increasing energy…
Learning reduced descriptions of chaotic many-body dynamics is fundamentally challenging: although microscopic equations are Markovian, collective observables exhibit strong memory and exponential sensitivity to initial conditions and…
How to learn an effective reinforcement learning-based model for control tasks from high-level visual observations is a practical and challenging problem. A key to solving this problem is to learn low-dimensional state representations from…
We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…
This work presents a two-stage physics-informed, data-driven constitutive modeling framework for hyperelastic soft materials undergoing progressive damage and failure. The framework is grounded in the concept of hyperelasticity with energy…
Stochastic resetting, the procedure of stopping and re-initializing random processes, has recently emerged as a powerful tool for accelerating processes ranging from queuing systems to molecular simulations. However, its usefulness is…
World models enable model-based planning through learned latent dynamics, but imagined rollouts become unstable as the planning horizon grows or the dynamics distribution shifts. We argue that this instability reflects two missing…
Hebbian learning theory is rooted in Pavlov's Classical Conditioning. While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently it has been numerically shown…
Memory retention challenges in deep neural architectures have ongoing limitations in the ability to process and recall extended contextual information. Token dependencies degrade as sequence length increases, leading to a decline in…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
We propose a general hybrid physics-informed machine learning framework for modeling nonlinear, history-dependent viscoelastic behavior under multiaxial cyclic loading. The approach is built on a generalized internal state variable-based…
The emergence of memory is a hallmark feature of non-Markovian dynamics. However, the type of memory -- classical or quantum -- required to realize certain dynamics remains unknown. We study the quantum homogenizer as a minimal model of…