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This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…
We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and…
Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach…
The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while piecewise-linear losses (like Hinge)…
Accurate semantic segmentation models typically require significant computational resources, inhibiting their use in practical applications. Recent works rely on well-crafted lightweight models to achieve fast inference. However, these…
Mesh-based numerical solvers are an important part in many design tool chains. However, accurate simulations like computational fluid dynamics are time and resource consuming which is why surrogate models are employed to speed-up the…
Physics simulations have become fundamental tools to study myriad engineering systems. As physics simulations often involve simplifications, their outputs should be calibrated using real-world data. In this paper, we present a…
Subsurface flow problems usually involve some degree of uncertainty. Consequently, uncertainty quantification is commonly necessary for subsurface flow prediction. In this work, we propose a methodology for efficient uncertainty…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Model merging offers an effective strategy to combine the strengths of multiple finetuned models into a unified model that preserves the specialized capabilities of each. Existing methods merge models in a global manner, performing…
Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…
Recent advances in autoregressive neural surrogate models have enabled orders-of-magnitude speedups in simulating dynamical systems. However, autoregressive models are generally prone to distribution drift: compounding errors in…
This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series. Using an experimental design of the low-and high-fidelity code levels, an original Gaussian process…