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In the last ten years, the phase-field method has gained much attention as a novel method to simulate fracture due to its straightforward way allowing to cover crack initiation and propagation without additional conditions. More recently,…
A statistical predictive model in which a high-dimensional time-series regenerates at the end of each day is used to model road traffic. Due to the regeneration, prediction is based on a daily modeling using a vector autoregressive model…
In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and…
Latent force models, a class of hybrid modeling approaches, integrate physical knowledge of system dynamics with a latent force - an unknown, unmeasurable input modeled as a Gaussian process. In this work, we introduce two optimal state…
Growing concerns regarding the operational usage of AI models in the real-world has caused a surge of interest in explaining AI models' decisions to humans. Reinforcement Learning is not an exception in this regard. In this work, we propose…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
Although reinforcement learning (RL) has tremendous success in many fields, applying RL to real-world settings such as healthcare is challenging when the reward is hard to specify and no exploration is allowed. In this work, we focus on…
We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We…
Standard regression techniques, while powerful, are often constrained by predefined, differentiable loss functions such as mean squared error. These functions may not fully capture the desired behavior of a system, especially when dealing…
Deep latent variable models have achieved significant empirical successes in model-based reinforcement learning (RL) due to their expressiveness in modeling complex transition dynamics. On the other hand, it remains unclear theoretically…
Contact-rich manipulation tasks with stiff frictional elements like connector insertion are difficult to model with rigid-body simulators. In this work, we propose a new approach for modeling these environments by learning a quasi-static…
In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a…
In dynamic simulation of complete wheel loaders, one interesting aspect, specific for the working task, is the momentary power distribution between drive train and hydraulics, which is balanced by the operator. This paper presents the…
This paper delves into designing stabilizing feedback control gains for continuous linear systems with unknown state matrix, in which the control is subject to a general structural constraint. We bring forth the ideas from reinforcement…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic…
In the paper, we discuss the reconstruction of scalar parameters in a linear diffusion equation with fractional in time differential operators and with additional nonlocal (convolution) terms, which incorporate memory effects in models.…
We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
One of the most notable aspects of mathematical modeling is that it sheds light on the complexities arising from changes in parameters and their real-world implications, thus gaining better insight into the dynamics of economic, political,…