Related papers: Discovering interpretable low-dimensional dynamics…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
We present a deep-learning Variational Encoder-Decoder (VED) framework for learning data-driven low-dimensional representations of the relationship between high-dimensional parameters of a physical system and the system's high-dimensional…
The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…
This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system…
The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in…
Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
How can we effectively encode evolving information over dynamic graphs into low-dimensional representations? In this paper, we propose DyRep, an inductive deep representation learning framework that learns a set of functions to efficiently…
We describe a set of novel methods for efficiently sampling high-dimensional parameter spaces of physical theories defined at high energies, but constrained by experimental measurements made at lower energies. Often, theoretical models such…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
The advent of big data has vast potential for discovery in natural phenomena ranging from climate science to medicine, but overwhelming complexity stymies insight. Existing theory is often not able to succinctly describe salient phenomena,…
We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a…
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
Extracting insight from the enormous quantity of data generated from molecular simulations requires the identification of a small number of collective variables whose corresponding low-dimensional free-energy landscape retains the essential…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
We introduce EMMA, a physics-informed multimodal framework that recovers all identifiable dynamical parameters of a system directly from raw video, audio, and image-based time-series observations. Unlike prior video-only approaches that…