Related papers: tLaSDI: Thermodynamics-informed latent space dynam…

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso…

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…

Coupling of physics across length and time scales plays an important role in the response of microstructured materials to external loads. In a multi-scale framework, unresolved (subgrid) meso-scale dynamics is upscaled to the homogenized…

The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear…

Thermodynamics, introduced over two centuries ago, remains foundational to our understanding of physical, chemical, biological, and engineering systems. Its principles are traditionally grounded in the statistical mechanics framework, which…

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…

In this work, we report an autoencoder-based 2D representation to classify a time-series as stochastic or non-stochastic, to understand the underlying physical process. Content-aware conversion of 1D time-series to 2D representation, that…

Latent factor analysis via dynamical systems (LFADS) is an RNN-based variational sequential autoencoder that achieves state-of-the-art performance in denoising high-dimensional neural activity for downstream applications in science and…

Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience…

Variational Autoencoders (VAEs) are powerful generative models for learning latent representations. Standard VAEs generate dispersed and unstructured latent spaces by utilizing all dimensions, which limits their interpretability, especially…

In real-world sequential decision making tasks like autonomous driving, robotics, and healthcare, learning from observed state-action trajectories is critical for tasks like imitation, classification, and clustering. For example,…

Language modeling has shown us that transformers can discover latent structure from context, but the dynamics of how they acquire different components of that structure remain poorly understood, leading to assertions that models just remix…

We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system…

In this work, we propose a data-driven method to discover the latent space and learn the corresponding latent dynamics for a collisional-radiative (CR) model in radiative plasma simulations. The CR model, consisting of high-dimensional…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

An autoencoder is a neural network which data projects to and from a lower dimensional latent space, where this data is easier to understand and model. The autoencoder consists of two sub-networks, the encoder and the decoder, which carry…

Novelty detection is commonly referred to as the discrimination of observations that do not conform to a learned model of regularity. Despite its importance in different application settings, designing a novelty detector is utterly complex…