Related papers: A critical note on back-and-forth Data Assimilatio…
We consider the statistical nonlinear inverse problem of recovering the absorption term $f>0$ in the heat equation $$ \partial_tu-\frac{1}{2}\Delta u+fu=0 \quad \text{on $\mathcal{O}\times(0,\textbf{T})$}\quad u = g \quad \text{on…
In fluorescence diffuse optical tomography (fDOT), the reconstruction of the fluorophore concentration inside the target body is usually carried out using a normalized Born approximation model where the measured fluorescent emission data is…
Data assimilation (DA) is integrated with machine learning in order to perform entirely data-driven online state estimation. To achieve this, recurrent neural networks (RNNs) are implemented as surrogate models to replace key components of…
Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…
Accurately simulating extended periodic systems is a central challenge in condensed matter physics. Neural quantum states (NQS) offer expressive wavefunctions for this task but face issues with scalability. In this work, we successfully…
We investigate several approaches to address the inverse problem that arises in the limited inverse Fourier transform (L-IDFT) of quasi-distributions. The methods explored include Tikhonov regularization, the Backus-Gilbert method, the…
We develop a general optimization-theoretic framework for Bregman-Variational Learning Dynamics (BVLD), a new class of operator-based updates that unify Bayesian inference, mirror descent, and proximal learning under time-varying…
Quantitative notions of bisimulation are well-known tools for the minimization of dynamical models such as Markov chains and ordinary differential equations (ODEs). In \emph{forward bisimulations}, each state in the quotient model…
We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier-Stokes equations of fluid dynamics, are characterized…
Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
Recent studies have shown that it is possible to combine machine learning methods with data assimilation to reconstruct a dynamical system using only sparse and noisy observations of that system. The same approach can be used to correct the…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
We propose, analyze, and test a novel continuous data assimilation two-phase flow algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed using coarse mesh observations, converge at an exponential rate…
Most existing federated learning algorithms are based on the vanilla FedAvg scheme. However, with the increase of data complexity and the number of model parameters, the amount of communication traffic and the number of iteration rounds for…
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE). Compared to integer order differential equation, FDE has the advantage that it can better…
We consider the inverse problem of reconstructing an unknown function $u$ from a finite set of measurements, under the assumption that $u$ is the trajectory of a transport-dominated problem with unknown input parameters. We propose an…