Related papers: Variational Data-Consistent Assimilation
In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…
Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the…
Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…
Real-time forecasting from streaming data poses critical challenges: handling non-stationary dynamics, operating under strict computational limits, and adapting rapidly without catastrophic forgetting. However, many existing approaches face…
This paper presents an Adaptive Dynamic Attribute and Rule (ADAR) framework designed to address the challenges posed by high-dimensional data in neuro-fuzzy inference systems. By integrating dual weighting mechanisms-assigning adaptive…
This paper focusses on the optimal implementation of a Mean Variance Estimation network (MVE network) (Nix and Weigend, 1994). This type of network is often used as a building block for uncertainty estimation methods in a regression…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…
Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations…
Incremental 4D-Var is a data assimilation algorithm used routinely at operational numerical weather predictions centers worldwide.This paper implements a new method for parallelizing incremental 4D-Var, the Randomized Incremental Optimal…
We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…
We describe a new method, full waveform inversion by model extension (FWIME) that recovers accurate acoustic subsurface velocity models from seismic data, when conventional methods fail. We leverage the advantageous convergence properties…
Data-driven machine learning (ML) models are reshaping weather forecasting and have shown the potential to accelerate and surpass traditional physics-based approaches, leading to a second revolution in the field after data assimilation.…
Conditional Variance Estimation (CVE) is a novel sufficient dimension reduction (SDR) method for additive error regressions with continuous predictors and link function. It operates under the assumption that the predictors can be replaced…
Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…
Diffusion models have recently achieved remarkable success in generative modeling, yet their training dynamics across different noise levels remain highly imbalanced, which can lead to inefficient optimization and unstable learning…
Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…
The Reynolds-averaged Navier-Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their…
Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…