Related papers: Greedy kernel methods for accelerating implicit in…

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

We propose a novel method for gradient-based optimization of black-box simulators using differentiable local surrogate models. In fields such as physics and engineering, many processes are modeled with non-differentiable simulators with…

Global aerodynamic design optimization using Euler or Navier-Stokes equations requires very reliable surrogate modeling techniques since the computational effort for the underlying flow simulations is usually high. In general, for such…

Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly…

Offline optimization has recently emerged as an increasingly popular approach to mitigate the prohibitively expensive cost of online experimentation. The key idea is to learn a surrogate of the black-box function that underlines the target…

Simulation techniques such as the finite element method are essential for designing electrical devices, but their computational cost can be prohibitive for repeated or real-time computations. Projection-based model order reduction…

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…

High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…

Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels…

We investigate a deep learning approach to efficiently perform Bayesian inference in partial differential equation (PDE) and integral equation models over potentially high-dimensional parameter spaces. The contributions of this paper are…

Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Simulators often provide the best description of real-world phenomena. However, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based…

In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric…