Related papers: Predicting partially observable dynamical systems …

Climate change exacerbates extreme weather events like heavy rainfall and flooding. As these events cause severe socioeconomic damage, accurate high-resolution simulation of precipitation is imperative. However, existing Earth System Models…

A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…

Data intensive applications often involve the analysis of large datasets that require large amounts of compute and storage resources. While dedicated compute and/or storage farms offer good task/data throughput, they suffer low resource…

Physics-informed deep learning has been developed as a novel paradigm for learning physical dynamics recently. While general physics-informed deep learning methods have shown early promise in learning fluid dynamics, they are difficult to…

Predicting the dynamics of complex systems is crucial for various scientific and engineering applications. The accuracy of predictions depends on the model's ability to capture the intrinsic dynamics. While existing methods capture key…

Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors…

We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…

Large ensembles of climate projections are essential for characterizing uncertainty in future climate and extreme weather events, yet computational constraints of numerical climate models limit ensemble sizes to a small number of…

Accurately predicting the dynamics of robotic systems is crucial for model-based control and reinforcement learning. The most common way to estimate dynamics is by fitting a one-step ahead prediction model and using it to recursively…

The advent and proliferation of social media have led to the development of mathematical models describing the evolution of beliefs/opinions in an ecosystem composed of socially interacting users. The goal is to gain insights into…

Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…

This paper presents a modified model predictive control (MPC) framework for real-time power system operation. The framework incorporates a diffusion model tailored for time series generation to enhance the accuracy of the load forecasting…

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution…

This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…

The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces a variant of stochastic interpolation (SI) for probabilistic…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

Predicting potential outcomes of interventions from observational data is crucial for decision-making in medicine, but the task is challenging due to the fundamental problem of causal inference. Existing methods are largely limited to point…