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Explainable artificial intelligence (AI) techniques are increasingly being explored to provide insights into why AI and machine learning (ML) models provide a certain outcome in various applications. However, there has been limited…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…
Before a car-following model can be applied in practice, it must first be validated against real data in a process known as calibration. This paper discusses the formulation of calibration as an optimization problem, and compares different…
We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces \cite{arXiv:1912.04234} by including the agents' body size. The influence of the body size on…
We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the…
Dealing with planning problems with both logical relations and numeric changes in real-world dynamic environments is challenging. Existing numeric planning systems for the problem often discretize numeric variables or impose convex…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent…
Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic…
We present a new backfitting algorithm estimating the complex structured non-parametric survival model of Scheike (2001) without having to use smoothing. The considered model is a non-parametric survival model with two time-scales that are…
Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the…
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…
With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications…
To increase the predictive power of a model, one needs to estimate its unknown parameters. Almost all parameter estimation techniques in ordinary differential equation models suffer from either a small convergence region or enormous…
Neuroscientists fit morphologically and biophysically detailed neuron simulations to physiological data, often using evolutionary algorithms. However, such gradient-free approaches are computationally expensive, making convergence slow when…
This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…
Cardiac muscle tissue exhibits highly non-linear hyperelastic and orthotropic material behavior during passive deformation. Traditional constitutive identification protocols therefore combine multiple loading modes and typically require…