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Flash floods in urban areas occur with increasing frequency. Detecting these floods would greatlyhelp alleviate human and economic losses. However, current flood prediction methods are eithertoo slow or too simplified to capture the flood…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
This work aims to improve fuel chamber injectors' performance in turbofan engines, thus implying improved performance and reduction of pollutants. This requires the development of models that allow real-time prediction and improvement of…
This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and…
There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…
Reliable predictions of critical phenomena, such as weather, wildfires and epidemics often rely on models described by Partial Differential Equations (PDEs). However, simulations that capture the full range of spatio-temporal scales…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…
Because of the impact of extreme heat waves and heat domes on society and biodiversity, their study is a key challenge. We specifically study long-lasting extreme heat waves, which are among the most important for climate impacts. Physics…
Short-term precipitation forecasting is essential for planning of human activities in multiple scales, ranging from individuals' planning, urban management to flood prevention. Yet the short-term atmospheric dynamics are highly nonlinear…
We propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents…
This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…
Fast and robust dynamic state estimation (DSE) is essential for accurately capturing the internal dynamic processes of power systems, and it serves as the foundation for reliably implementing real-time dynamic modeling, monitoring, and…
Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…
This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…
Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model…
Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…
Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…