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Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…
Accurately forecasting the weather is a key requirement for climate change mitigation. Data-driven methods offer the ability to make more accurate forecasts, but lack interpretability and can be expensive to train and deploy if models are…
A basic requirement for a mathematical model is often that its solution (output) shouldn't change much if the model's parameters (input) are perturbed. This is important because the exact values of parameters may not be known and one would…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
We study the problem of designing optimal learning and decision-making formulations when only historical data is available. Prior work typically commits to a particular class of data-driven formulation and subsequently tries to establish…
Parametric models abstract part of the specification of dynamical models by integral parameters. They are for example used in computational systems biology, notably with parametric regulatory networks, which specify the global architecture…
Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…
Models for vehicle dynamics play an important role in maneuver planning for automated driving. They are used to derive trajectories from given control inputs, or to evaluate a given trajectory in terms of constraint violation or optimality…
Across scientific domains, generating new models or optimizing existing ones while meeting specific criteria is crucial. Traditional machine learning frameworks for guided design use a generative model and a surrogate model (discriminator),…
Learned dynamics models combined with both planning and policy learning algorithms have shown promise in enabling artificial agents to learn to perform many diverse tasks with limited supervision. However, one of the fundamental challenges…
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…
Autonomous vehicles need to model the behavior of surrounding human driven vehicles to be safe and efficient traffic participants. Existing approaches to modeling human driving behavior have relied on both data-driven and rule-based…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
Data-driven design is making headway into a number of application areas, including protein, small-molecule, and materials engineering. The design goal is to construct an object with desired properties, such as a protein that binds to a…
The difficulty of solving a multi-objective optimization problem is impacted by the number of objectives to be optimized. The presence of many objectives typically introduces a number of challenges that affect the choice/design of…
With machine learning models being increasingly used to aid decision making even in high-stakes domains, there has been a growing interest in developing interpretable models. Although many supposedly interpretable models have been proposed,…
The fine-tuning of pre-trained models has become ubiquitous in generative AI, computer vision, and robotics. Although much attention has been paid to improving the efficiency of fine-tuning model, there has been less scholarship around…
Machine learning models built on datasets containing discriminative instances attributed to various underlying factors result in biased and unfair outcomes. It's a well founded and intuitive fact that existing bias mitigation strategies…
Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…