Related papers: Predictability in Spatially Extended Systems with …
Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…
This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
This paper studies stabilities of stochastic differential equation (SDE) driven by time-changed L\'evy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics,…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…
We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we realise a variational formulation, solving a vast class of…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are…
Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…