SDA method reduces memory and time for assimilating noisy geophysical data.
problem Challenges in identifying state trajectories of high-dimensional geophysical systems.
method Score-based data assimilation with modified score network architecture.
result Promising results for a two-layer quasi-geostrophic model.
EnSF uses image inpainting to handle partial observations in data assimilation.
problem Data assimilation challenges with partial observations.
method EnSF integrates image inpainting with diffusion models to predict unobserved states.
result EnSF successfully tracks SQG dynamics with partial observations.
LD-EnSF speeds up data assimilation with sparse observations.
problem Efficiently assimilate sparse and noisy data into complex dynamical systems.
method LD-EnSF uses latent dynamics networks and history-aware LSTM encoders to process sparse observations without full-space simulations.
result Achieves significant speedups over existing methods while maintaining high accuracy.
Simulator imperfection, often known as model error, is ubiquitous in practical data assimilation problems. Despite the enormous efforts dedicated to addressing this problem, properly handling simulator imperfection in data assimilation remains to be a challenging task. In this work, we propose an approach to dealing wi…
Machine learning improves solving inverse problems and integrating data.
problem Solving complex inverse problems and integrating data effectively.
method Integrates machine learning techniques with inverse problems and data assimilation.
result Demonstrates machine learning's potential to enhance these fields.
New method calibrates predictions in chaotic systems using variational inference.
problem Uncertainty in data assimilation for chaotic systems.
method Variational inference applied to multivariate Gaussian distribution.
result Nearly perfectly calibrated predictions in chaotic Lorenz-96 dynamics.
Combines machine learning and data assimilation for improved forecasting.
problem Improving forecast accuracy with noisy observations.
method Sequentially learns a machine-learning model using an ensemble Kalman filter.
result The combined model achieves good forecast skill and computational efficiency.
This paper learns state, dynamics, and filtering algorithms together for data assimilation.
problem Costly parameter tuning and inaccurate dynamics models hinder data assimilation algorithms.
method Auto-differentiable data assimilation framework that learns state, dynamics, and parameters via gradient-based optimization.
result Several data assimilation methods can be learned or tuned within this framework.
Stochastic methods improve data assimilation with high-frequency sensor data.
problem Computational challenges in data assimilation with high-frequency sensor data.
method Adapted stochastic approximation methods to handle high-frequency observations.
result Produces high-quality estimates using all observations without compromising statistical accuracy.
AD-EnKFs use machine learning to improve data assimilation in high-dimensional systems.
problem Data assimilation in high-dimensional, unknown dynamics systems.
method Auto-differentiable ensemble Kalman filters blending machine learning and ensemble Kalman filters.
result AD-EnKFs outperform existing methods in the Lorenz-96 model.
Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.
problem Challenges of non-Gaussian statistics in data assimilation.
method Triangular measure transport with P-spline basis functions and an information criterion.
result Automatic selection of parsimonious parametrization for efficient adaptation.
New method combines neural networks and data assimilation for indoor air quality prediction.
problem Accurate and fast prediction of indoor air quality using real-time data.
method Combines Data Assimilation and Machine Learning using a Convolutional neural network and Long-Short-Term-Memory.
result Improved accuracy of dynamic system representation by integrating real data.
EnCF improves data assimilation for implicit, non-smooth observations.
problem Data assimilation challenges with implicit, many-to-one observations.
method EnCF uses a stochastic controlled flow to update forecast distributions.
result EnCF outperforms Kalman filters for non-Gaussian, implicit observations.
Proposes a new method for data assimilation using closed-form conditional diffusion models.
problem Data assimilation for systems with complex, non-Gaussian probability distributions.
method Uses kernel density estimation to model joint distributions and leverages the score function for efficient evaluation.
result Outperforms ensemble Kalman and particle filters in nonlinear data assimilation problems.
New method for data assimilation using score-based models.
problem Bayesian inverse problem of identifying plausible state trajectories.
method Score-based data assimilation, learning a score-based generative model of state trajectories.
result Effective method for zero-shot observation scenarios.
CG-EnKF and NS-EnKF outperform deep learning-based SF in data assimilation.
problem Data assimilation with non-linear perturbations.
method Two non-linear extensions of EnKF: CG-EnKF and NS-EnKF.
result CG-EnKF and NS-EnKF outperform SF in high-dimensional multiscale data assimilation.
EnFF uses flows to speed up DA in high dimensions.
problem Efficiently assimilating noisy data in high-dimensional systems.
method Flow Matching (FM) for training-free, scalable data assimilation.
result EnFF accelerates DA with improved cost-accuracy tradeoffs and scalability.
Prequential posteriors tackle data assimilation for deep generative forecasting models.
problem Challenges in assimilating data into deep generative forecasting models due to intractable likelihood functions.
method Introduces prequential posteriors based on a predictive-sequential loss function, proving consistency under mild conditions, and using parallelizable SMC samplers for scalable inference.
result Prequential posteriors concentrate around parameters with optimal predictive performance, validating method on synthetic and real-world datasets.
Latent-EnSF improves data assimilation for high-dimensional systems with sparse observations.
problem Challenges in high-dimensional, nonlinear Bayesian filtering with sparse observations.
method A novel data assimilation method using latent representations and a coupled VAE for efficient state encoding and reconstruction.
result Latent-EnSF outperforms traditional methods in accuracy, convergence, and efficiency for complex systems.
ACI uses Bayesian data assimilation to trace causes from effects in complex systems.
problem Capturing instantaneous, time-evolving causal relationships in complex, high-dimensional systems.
method Assimilative causal inference (ACI) leverages Bayesian data assimilation to trace causes backward from observed effects.
result ACI provides online tracking of causal roles that may reverse intermittently and reveals how far effects propagate.
EnKF's update is shown to be similar to Matheron's method in Gaussian process regression.
problem Data assimilation in high-dimensional systems.
method Empirical Matheron update applied to EnKF.
result Ensemble Kalman Filter's update is equivalent to an empirical Matheron update.
A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future states. The method consists in applying iteratively a data assimilation step, here…
SOAD model improves data assimilation for nonlinear systems.
problem Challenges in classical data assimilation with high nonlinearity.
method State-Observation Augmented Diffusion (SOAD) model for data-driven assimilation.
result SOAD model matches true posterior distribution under mild assumptions.
DAISI improves data assimilation for complex systems with noisy observations.
problem Limited accuracy of classical DA methods in complex, nonlinear systems.
method Generative models with inverse sampling for flexible probabilistic inference.
result DAISI achieves accurate filtering results in challenging nonlinear systems.
Epidemiological model updates infection rates in China, US, Italy.
problem Evaluate policy interventions for mitigating the 2019-nCov pandemic.
method Custom SITR model with variational data assimilation for real-time updates.
result Model robust to initial conditions, infers infection numbers and parameters.
This paper develops nudging algorithms using learned surrogates for state estimation in dynamical systems.
problem Estimating the state of a dynamical system from partial observations when dynamics are unknown or expensive to simulate.
method Unified finite-dimensional analysis of nudging algorithms employing learned surrogate models of the dynamics.
result Nudging algorithms with surrogate models retain exponential convergence up to an explicit error floor.
Neural architecture improves geophysical data assimilation with uncertainty quantification.
problem Improving geophysical data interpolation with uncertainty quantification.
method Neural variational data assimilation with SPDE priors.
result Demonstrated improved performance and uncertainty quantification.
New method combines machine learning with data assimilation for model error correction.
problem Correcting model errors using sparse and noisy observations.
method Hybrid machine learning and data assimilation methods.
result Tendency correction outperforms resolvent correction in data assimilation experiments.
Deep learning speeds up pressure prediction in carbon storage reservoirs.
problem Accurately forecasting reservoir pressure in geologic carbon storage projects with sparse well data.
method Combining InSAR surface displacement data with deep learning and data assimilation techniques.
result Workflow can predict reservoir pressure with high efficiency and uncertainty quantification.
DA-PredGAN uses GANs for accurate COVID-19 spread predictions and data assimilation.
problem Predicting and understanding the spread of COVID-19.
method Generative adversarial network (GAN) for predictions and data assimilation.
result DA-PredGAN accurately predicts and assimilates COVID-19 spread data.
MEDIDA discovers model errors in chaotic systems using sparse regression and data assimilation.
problem Model errors in chaotic systems lead to significant discrepancies between model predictions and real-world states.
method MEDIDA combines Bayesian sparse regression and data assimilation to estimate and interpret model errors from noisy observations.
result MEDIDA successfully identifies different types of model errors in the chaotic Kuramoto-Sivashinsky system.
Proposes LAE-EnKF for improved nonlinear data assimilation.
problem Performance of EnKF deteriorates for strongly nonlinear dynamics.
method Reformulates assimilation in a learned latent space with linear dynamics.
result LAE-EnKF yields more accurate and stable assimilation.
Data assimilation for subsurface flow using latent diffusion models shows that ensemble Kalman methods may overestimate posterior uncertainty, while Monte Carlo sampling is more reliable.
problem Data assimilation for subsurface flow
method Ensemble Kalman smoother and Markov chain Monte Carlo sampling
result Monte Carlo sampling is more reliable than ensemble Kalman methods
Unified error analysis for low-rank approximation improves data assimilation performance.
problem Analyzing the error in low-rank approximation methods for data assimilation.
method Unified stochastic analysis framework for Frobenius norm error bounds on centered and non-standard Gaussian matrices.
result Unified bounds provide clearer interpretations and enable better practical choices for covariance matrices.
Develops theory for data-driven methods in dynamical systems.
problem Lack of analysis for data-driven methods in dynamical systems.
method Establishes existence of mapping and properties of operator learning architecture.
result Novel universal approximation theorems for smoothing and forecasting.
Novel method for nonlinear data assimilation using Langevin sampling.
problem Nonlinear data assimilation challenges in Bayesian filtering.
method Score-based sequential Langevin sampling (SSLS) with dynamic models and annealing.
result Asymptotic stability and error bounds for local posterior sampling.
New methods use RL and DA to improve dosing precision and reduce side effects.
problem Improving precision and safety of anticancer drug dosing.
method Bayesian data assimilation and reinforcement learning.
result Significantly reduces incidence of severe side effects.
A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent networ…
This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.
problem Maintaining critical invariants like mass, stoichiometric balance, and charge in non-Gaussian data assimilation.
method Introducing a novel class of nonlinear ensemble filters using measure transport theory.
result Recovery of a constrained Kalman filter for Gaussian settings and combination with regularization techniques.
We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and biological sciences, systematically transfers information in observations to a model of …
We analyze errors in filtering algorithms using optimal transport.
problem Estimation errors in optimal transport-based filtering algorithms.
method Systematic analysis of estimation errors for conditional Brenier maps.
result Demonstrates effectiveness and practical potential of the optimal transport filtering algorithm.
Artificial neural networks estimate model parameters from observations, reducing model errors.
problem Estimating parameters of convection-permitting models from observations.
method Training Bayesian neural networks and point estimate neural networks on atmospheric state observations.
result Artificial neural networks can estimate model parameters and their statistics.
A new particle filter uses diffusion models to improve state estimation from noisy data.
problem Sequentially estimating the state of a dynamical system from noisy and incomplete observations.
method Uses a diffusion model to simulate and predict system dynamics, incorporating noisy observations to refine predicted states.
result An unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference fro…
With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model parameters in the equations are either assumed to be known or have a linear depen…
Hybrid model improves weather forecasting accuracy.
problem Combining physics and machine learning for better weather predictions.
method Offline and online training of a neural network to correct model errors in the IFS.
result The hybrid model reduces forecast errors and improves accuracy.
Develops Φ-DVAE for assimilating unstructured data into physical models.
problem Challenges in incorporating unstructured data into physical models.
method Physics-informed dynamical variational autoencoder (Φ-DVAE) combining latent state-space model and VAE. result Demonstrates data-efficient dynamics encoding with competitive performance and uncertainty quantification.
A new ML-based filter improves data assimilation for nonlinear systems.
problem Improving data assimilation for nonlinear systems using ensemble methods.
method Developed a machine learning-based conditional mean filter (ML-EnCMF) integrating ANN and linear functions.
result ML-EnCMF outperforms EnKF and likelihood-based EnCMF in nonlinear systems.