Related papers: Time-Dependent PDE-Constrained Optimization via We…
Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…
Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…
Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…
We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms…
Numerical solving parameterised partial differential equations (P-PDEs) is highly practical yet computationally expensive, driving the development of reduced-order models (ROMs). Recently, methods that combine latent space identification…
Design optimisation offers the potential to develop lightweight aircraft structures with reduced environmental impact. Due to the high number of design variables and constraints, these challenges are typically addressed using gradient-based…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The…
Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential…
Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…
Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…
This paper provides a unifying theoretical framework for stochastic optimization algorithms by means of a latent stochastic variational problem. Using techniques from stochastic control, the solution to the variational problem is shown to…
The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines. A significant challenge arises from noise-corrupted measurements,…
Traditional partial differential equation (PDE) solvers can be computationally expensive, which motivates the development of faster methods, such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning and Bayesian ROM.…