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Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
Accurate free energy representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy model by training a neural network on DFT-informed…
Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…
Recent years have witnessed a surge of experimental and theoretical interest in controlling the properties of matter, such as its chemical reactivity, by confining it in optical cavities, where the enhancement of the light-matter coupling…
We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…
In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…
Identifying partial differential equations (PDEs) from data is crucial for understanding the governing mechanisms of natural phenomena, yet it remains a challenging task. We present an extension to the ARGOS framework, ARGOS-RAL, which…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
We develop and apply a learning framework for parameter estimation in initial value problems that are assessed only indirectly via aggregate data such as sample means and/or standard deviations. Our comprehensive framework follows Bayesian…
Quantum Monte Carlo integration, a quantum algorithm for calculating expectations that provides a quadratic speed-up compared to its classical counterpart, is now attracting increasing interest in the context of its industrial and…
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
We generalize the multilevel Monte Carlo (MLMC) method of Giles to the simulation of systems of particles that interact via a mean field. When the number of particles is large, these systems are described by a McKean-Vlasov process - a…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…