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Locational marginal emissions rates (LMEs) estimate the rate of change in emissions due to a small change in demand in a transmission network, and are an important metric for assessing the impact of various energy policies or interventions.…
The integration of machine learning (ML) with traditional physics-based models is reshaping the landscape of weather and climate prediction. On their own, ML-based and physics-based approaches each have significant benefits - but also…
A centralized model predictive controller (MPC), which is unaware of local uncertainties, for an affine discrete time nonlinear system is presented. The local uncertainties are assumed to be matched, bounded and structured. In order to…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
Standard approaches to controlling dynamical systems involve biologically implausible steps such as backpropagation of errors or intermediate model-based system representations. Recent advances in machine learning have shown that…
This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra.…
Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse-grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral…
This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
We consider the commonly encountered situation (e.g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous…
Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable, and isotropic elastic solid, which is immersed in a homogeneous compressible air or fluid. The paper concerns the numerical solution for such an…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
The increasing frequency of extreme weather events due to global climate change urges accurate weather prediction. Recently, great advances have been made by the \textbf{end-to-end methods}, thanks to deep learning techniques, but they face…
Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…
Recent developments dedicated to the building of multiscale mechanical and chemical constitutive laws for energetic molecular crystals are presented and discussed. In particular, various tools have been specifically incorporated in…
High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the…
In climate change study, the infrared spectral signatures of climate change have recently been conceptually adopted, and widely applied to identifying and attributing atmospheric composition change. We propose a Bayesian hierarchical model…
Intelligent fault diagnosis has become an indispensable technique for ensuring machinery reliability. However, existing methods suffer significant performance decline in real-world scenarios where models are tested under unseen working…
We extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are…