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Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…
In this study, we explore the application of Physics-Informed Neural Networks (PINNs) to the analysis of bifurcation phenomena in ecological migration models. By integrating the fundamental principles of diffusion-advection-reaction…
Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial…
Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…
The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this…
Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity…
Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization,…
We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the…
Simulation-Based Inference (SBI) is a promising Bayesian inference framework that alleviates the need for analytic likelihoods to estimate posterior distributions. Recent advances using neural density estimators in SBI algorithms have…
Semi-implicit variational inference (SIVI) extends traditional variational families with semi-implicit distributions defined in a hierarchical manner. Due to the intractable densities of semi-implicit distributions, classical SIVI often…
The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and…
Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard,…
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include…
Full-waveform inversion (FWI) is a widely used technique in seismic processing to produce high resolution Earth models that fully explain the recorded seismic data. FWI is a local optimisation problem which aims to minimise in a…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
Partial differential equations and variational problems can be solved with physics informed neural networks (PINNs). The unknown field is approximated with neural networks. Minimizing the residuals of the static Maxwell equation at…
We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…