Related papers: Extending a Physics-Based Constitutive Model using…
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…
Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…
The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
The identification of constitutive laws is ubiquitous in engineering: in modeling of materials where experimental data are fitted to mathematical models or learning surrogate models to beat the FE\textsuperscript{2} computational cost of…
Deformable object manipulation remains a challenging task in robotics research. Conventional techniques for parameter inference and state estimation typically rely on a precise definition of the state space and its dynamics. While this is…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
Diffusion models have emerged as powerful tools for high-quality image generation and editing, but guiding these models to produce specific outputs remains a challenge. Conventional approaches rely on conditioning mechanisms, such as text…
Hydrogen enhanced cracking is one of the many failure mechanisms in metals depending on the corrosive environment. In the presented work, a multiscale constitutive model has been presented for hydrogen enhanced intergranular cracking in…
Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…
Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…
In this paper, we propose a nonlinear probabilistic generative model of Koopman mode decomposition based on an unsupervised Gaussian process. Existing data-driven methods for Koopman mode decomposition have focused on estimating the…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
Deep learning-based medical image processing algorithms require representative data during development. In particular, surgical data might be difficult to obtain, and high-quality public datasets are limited. To overcome this limitation and…
Generative artificial intelligence models learn probability distributions from data and produce novel samples that capture the salient properties of their training sets. Proteins are particularly attractive for such approaches given their…
In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The DEs are typically nonlinear and difficult to analyze,…
Differentiable physics modeling combines physics models with gradient-based learning to provide model explicability and data efficiency. It has been used to learn dynamics, solve inverse problems and facilitate design, and is at its…
Existing data-driven methods for draping garments over human bodies, despite being effective, cannot handle garments of arbitrary topology and are typically not end-to-end differentiable. To address these limitations, we propose an…
Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a…