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Molecular dynamics simulations are powerful tools to extract the microscopic mechanisms characterizing the properties of soft materials. We recently introduced machine learning surrogates for molecular dynamics simulations of soft materials…
Surrogate models are data-based approximations of computationally expensive simulations that enable efficient exploration of the model's design space and informed decision-making in many physical domains. The usage of surrogate models in…
With the development of artificial intelligence, simulation-based optimization problems, which present a significant challenge in the process systems engineering community, are increasingly being addressed with the surrogate-based…
The active learning (AL) technique, one of the state-of-the-art methods for constructing surrogate models, has shown high accuracy and efficiency in forward uncertainty quantification (UQ) analysis. This paper provides a comprehensive study…
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…
This paper aims to understand whether machine learning models should be trained using cost-sensitive surrogates or cost-agnostic ones (e.g., cross-entropy). Analyzing this question through the lens of $\mathcal{H}$-calibration, we find that…
In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex…
We study sigma-additive set functions defined on a hereditary subclass of a sigma-algebra and taken values in the extended real line. Analogs of the Jordan decomposition theorem and the Radon-Nikodym theorem are obtained.
The topology optimization of artificial neural networks can be particularly difficult if the fitness evaluations require expensive experiments or simulations. For that reason, the optimization methods may need to be supported by surrogate…
Data-driven surrogate models of dynamical systems based on the extended dynamic mode decomposition are nowadays well-established and widespread in applications. Further, for non-holonomic systems exhibiting a multiplicative coupling between…
Surrogate markers are often used in clinical trials to evaluate treatment effects when primary outcomes are costly, invasive, or take a long time to observe. However, reliance on surrogates can lead to the surrogate paradox, where a…
A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…
Surrogate models are of high interest for many engineering applications, serving as cheap-to-evaluate time-efficient approximations of black-box functions to help engineers and practitioners make decisions and understand complex systems. As…
Robins and Richardson (2010) reformulated mediation analysis by decomposing treatments into multiple components and examining separable effects of each component. While this approach is increasingly popular, existing work has analyzed…
When minimizing the empirical risk in binary classification, it is a common practice to replace the zero-one loss with a surrogate loss to make the learning objective feasible to optimize. Examples of well-known surrogate losses for binary…
Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…
There is a high interest in accelerating multiscale models using data-driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational…
We propose an extension to time series with several simultaneously measured variables of the nonlinearity test, which combines the redundancy -- linear redundancy approach with the surrogate data technique. For several variables various…
The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems,…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…