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Partial differential equations often contain unknown functions that are difficult or impossible to measure directly, hampering our ability to derive predictions from the model. Workflows for recovering scalar PDE parameters from data are…
Deep learning-based reconstruction of positron emission tomography(PET) data has gained increasing attention in recent years. While these methods achieve fast reconstruction,concerns remain regarding quantitative accuracy and the presence…
Usually, clinicians assess the correct hemodynamic behavior and fetal well-being during the gestational age thanks to their professional expertise, with the support of some indices defined for Doppler fetal waveforms. Although this approach…
Patlak model is widely used in 18F-FDG dynamic positron emission tomography (PET) imaging, where the estimated parametric images reveal important biochemical and physiology information. Because of better noise modeling and more information…
The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood…
Photomultiplier tubes (PMTs) are widely employed in particle and nuclear physics experiments. The accuracy of PMT waveform reconstruction directly impacts the detector's spatial and energy resolution. A key challenge arises when multiple…
In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
The promising outcomes of dynamical system identification techniques, such as SINDy [Brunton et al. 2016], highlight their advantages in providing qualitative interpretability and extrapolation compared to non-interpretable deep neural…
In this paper, we review physics- and data-driven reconstruction techniques for simultaneous positron emission tomography (PET) / magnetic resonance imaging (MRI) systems, which have significant advantages for clinical imaging of cancer,…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
In the paper, we propose an analytical and numerical approach to identify scalar parameters (coefficients, orders of fractional derivatives) in the multi-term fractional differential operator in time, $\mathbf{D}_t$. To this end, we analyze…
We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…
Dynamical systems, for instance in model predictive control, often contain unknown parameters, which must be determined during system operation. Online or on-the-fly parameter identification methods are therefore necessary. The challenge of…
We present a novel approach to system identification (SI) using deep learning techniques. Focusing on parametric system identification (PSI), we use a supervised learning approach for estimating the parameters of discrete and…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative…
We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…
Pedestrian Attribute Recognition (PAR) is a challenging task as models are required to generalize across numerous attributes in real-world data. Traditional approaches focus on complex methods, yet recognition performance is often…