Related papers: Predicting the Energy Landscape of Stochastic Dyna…
Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective…
Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the…
A significant challenge in nature-inspired algorithmics is the identification of specific characteristics of problems that make them harder (or easier) to solve using specific methods. The hope is that, by identifying these characteristics,…
Accurate and efficient fluid flow models are essential for applications relating to many physical phenomena including geophysical, aerodynamic, and biological systems. While these flows may exhibit rich and multiscale dynamics, in many…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Despite deep-learning being state-of-the-art for data-driven model predictions, it has not yet found frequent application in ecology. Given the low sample size typical in many environmental research fields, the default choice for the…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…
Energy-based modeling is a promising approach to unsupervised learning, which yields many downstream applications from a single model. The main difficulty in learning energy-based models with the "contrastive approaches" is the generation…
A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…
Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
The long-standing, dominant approach to robotic obstacle negotiation relies on mapping environmental geometry to avoid obstacles. However, this approach does not allow for traversal of cluttered obstacles, hindering applications such as…
Exploring molecular energy landscapes and identifying ground-state conformations are central challenges in computational chemistry. However, generating diverse low-energy conformers from molecular graphs remains expensive with traditional…
A Potts model and the Replica Exchange Wang-Landau algorithm are used to construct an energy landscape for a crystalline solid containing surfaces and grain boundaries. The energy landscape is applied to an equation of motion from the…
Landscapes are meaningful ecological units that strongly depend on the environmental conditions. Such dependencies between landscapes and the environment have been noted since the beginning of Earth sciences and cast into conceptual models…
The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular…
The dynamics of individual colloidal particles in random potential energy landscapes were investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a…
Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor…
The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems. An exact…