Related papers: Predicting rare events using neural networks and s…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have…
Understanding extreme events and their probability is key for the study of climate change impacts, risk assessment, adaptation, and the protection of living beings. Forecasting the occurrence probability of extreme heatwaves is a primary…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well.…
Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition…
We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic…
Optimization of decision problems in stochastic environments is usually concerned with maximizing the probability of achieving the goal and minimizing the expected episode length. For interacting agents in time-critical applications,…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…
Recurrent neural networks for language models like long short-term memory (LSTM) have been utilized as a tool for modeling and predicting long term dynamics of complex stochastic molecular systems. Recently successful examples on learning…
In this paper, we present a novel Feynman-Kac formula and investigate learning-based methods for approximating general nonlinear time-dependent Schr\"odinger equations which may be high-dimensional. Our formulation integrates both the…
The analysis of extremes in climate models is hindered by the lack of statistics due to the computational costs required to run simulations long enough to sample rare events. We demonstrate how rare event algorithms can improve the…
Stochastic dynamical systems provide essential mathematical frameworks for modeling complex real-world phenomena. The Fokker-Planck-Kolmogorov (FPK) equation governs the evolution of probability density functions associated with stochastic…
In this work, we consider the numerical estimation of the probability for a stochastic process to hit a set B before reaching another set A. This event is assumed to be rare. We consider reactive trajectories of the stochastic Allen-Cahn…
Predicting the occurence of rare and extreme events in complex systems is a well-known problem in non-equilibrium physics. These events can have huge impacts on human societies. New approaches have emerged in the last ten years, which…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
Rare weather and climate events, such as heat waves and floods, can bring tremendous social costs. Climate data is often limited in duration and spatial coverage, and climate forecasting has often turned to simulations of climate models to…
Making the most of multispectral image time-series is a promising but still relatively under-explored research direction because of the complexity of jointly analyzing spatial, spectral and temporal information. Capturing and characterizing…