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Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a…
Highly accurate numerical or physical experiments are often time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide…
Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and…
We present methods for emulating the matter power spectrum by combining information from cosmological $N$-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter…
In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate…
A multi-fidelity regression model is proposed for combining multiple datasets with different fidelities, particularly abundant low-fidelity data and scarce high-fidelity observations. The model builds upon recent multi-fidelity frameworks…
Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy…
Multi-fidelity methods combine inexpensive low-fidelity simulations with costly but highfidelity simulations to produce an accurate model of a system of interest at minimal cost. They have proven useful in modeling physical systems and have…
High-resolution simulation models are essential for representing complex physical systems, yet their substantial computational cost severely limits the number of feasible high-fidelity (HF) evaluations. This problem is often addressed…
Multi-fidelity methods combine inexpensive low-fidelity simulations with costly but high-fidelity simulations to produce an accurate model of a system of interest at minimal cost. They have proven useful in modeling physical systems and…
In this work, we consider the general problem of constructing a neural network surrogate model using multi-fidelity information. Motivated by error-complexity estimates for ReLU neural networks, we formulate the correlation between an…
Multi-fidelity models provide a framework for integrating computational models of varying complexity, allowing for accurate predictions while optimizing computational resources. These models are especially beneficial when acquiring…
Operator learning frameworks, because of their ability to learn nonlinear maps between two infinite dimensional functional spaces and utilization of neural networks in doing so, have recently emerged as one of the more pertinent areas in…
In this work, we propose a network which can utilize computational cheap low-fidelity data together with limited high-fidelity data to train surrogate models, where the multi-fidelity data are generated from multiple underlying models. The…
Computer simulations have become essential for analyzing complex systems, but high-fidelity simulations often come with significant computational costs. To tackle this challenge, multi-fidelity computer experiments have emerged as a…
Neural operators or emulators for PDEs trained on data from numerical solvers are conventionally assumed to be limited by their training data's fidelity. We challenge this assumption by identifying "emulator superiority," where neural…
We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. Besides requiring significantly less trainable parameters than equivalent fully…
In the context of optimization approaches to engineering applications, time-consuming simulations are often utilized which can be configured to deliver solutions for various levels of accuracy, commonly referred to as different fidelity…
When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time dependent problems in engineering…