The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the beginning of the forecast. Data assimilation methods are used to infer these initial conditions by systematically combining noisy, incomplete observations and numerical models of system dynamics to produce highly effective estimation schemes. We introduce a self-supervised framework, which we call \textit{amortized assimilation}, for learning to assimilate in dynamical systems. Amortized assimilation combines deep learning-based denoising with differentiable simulation, using independent neural networks to assimilate specific observation types while connecting the gradient flow between these sub-tasks with differentiable simulation and shared recurrent memory. This hybrid architecture admits a self-supervised training objective which is minimized by an unbiased estimator of the true system state even in the presence of only noisy training data. Numerical experiments across several chaotic benchmark systems highlight the improved effectiveness of our approach compared to widely-used data assimilation methods.

The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the beginning of the forecast. Data assimilation methods are used to infer these initial conditions by systematically combining noisy, incomplete observations and numerical models of system dynamics to produce highly effective estimation schemes. We introduce a self-supervised framework, which we call \textit{amortized assimilation}, for learning to assimilate in dynamical systems. Amortized assimilation combines deep learning-based denoising with differentiable simulation, using independent neural networks to assimilate specific observation types while connecting the gradient flow between these sub-tasks with differentiable simulation and shared recurrent memory. This hybrid architecture admits a self-supervised training objective which is minimized by an unbiased estimator of the true system state even in the presence of only noisy training data.

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior physical knowledge. The size of the systems involved and the complexity of the underlying physical equations make it a challenging task from a computational point of view. Neural networks represent a promising method of emulating the physics at low cost, and therefore have the potential to considerably improve and accelerate data assimilation. In this work, we introduce a deep learning approach where the physical system is modeled as a sequence of coarse-to-fine Gaussian prior distributions parametrized by a neural network. This allows us to define an assimilation operator, which is trained in an end-to-end fashion to minimize the reconstruction error on a dataset with different observation processes. We illustrate our approach on chaotic dynamical physical systems with sparse observations, and compare it to traditional variational data assimilation methods.

Accurate and timely prediction of crop growth is of great significance to ensure crop yields and researchers have developed several crop models for the prediction of crop growth. However, there are large difference between the simulation results obtained by the crop models and the actual results, thus in this paper, we proposed to combine the simulation results with the collected crop data for data assimilation so that the accuracy of prediction will be improved. In this paper, an EnKF-LSTM data assimilation method for various crops is proposed by combining ensemble Kalman filter and LSTM neural network, which effectively avoids the overfitting problem of existing data assimilation methods and eliminates the uncertainty of the measured data. The verification of the proposed EnKF-LSTM method and the comparison of the proposed method with other data assimilation methods were performed using datasets collected by sensor equipment deployed on a farm.

Understanding and predicting people flow in urban areas is useful for decision-making in urban planning and marketing strategies. Traditional methods for understanding people flow can be divided into measurement-based approaches and simulation-based approaches. Measurement-based approaches have the advantage of directly capturing actual people flow, but they face the challenge of data imperfection. On the other hand, simulations can obtain complete data on a computer, but they only consider some of the factors determining human behavior, leading to a divergence from actual people flow. Both measurement and simulation methods have unresolved issues, and combining the two can complementarily overcome them. This paper proposes a method that applies data assimilation, a fusion technique of measurement and simulation, to agent-based simulation. Data assimilation combines the advantages of both measurement and simulation, contributing to the creation of an environment that can reflect real people flow while acquiring richer data. The paper verifies the effectiveness of the proposed method in a virtual environment and demonstrates the potential of data assimilation to compensate for the three types of imperfection in people flow measurement techniques. These findings can serve as guidelines for supplementing sparse measurement data in physical environments.

The generation of initial conditions via accurate data assimilation is crucial for reliable weather forecasting and climate modeling. We propose the DiffDA as a machine learning based data assimilation method capable of assimilating atmospheric variables using predicted states and sparse observations. We adapt the pretrained GraphCast weather forecast model as a denoising diffusion model. Our method applies two-phase conditioning: on the predicted state during both training and inference, and on sparse observations during inference only. As a byproduct, this strategy also enables the post-processing of predictions into the future, for which no observations are available. Through experiments based on a reanalysis dataset, we have verified that our method can produce assimilated global atmospheric data consistent with observations at 0.25degree resolution. The experiments also show that the initial conditions that are generated via our approach can be used for forecast models with a loss of lead time of at most 24 hours when compared to initial conditions of state-of-the-art data assimilation suites. This enables to apply the method to real world applications such as the creation of reanalysis datasets with autoregressive data assimilation.

Identification of unknown physical processes and parameters of groundwater contaminant sources is a challenging task due to their ill-posed and non-unique nature. Numerous works have focused on determining nonlinear physical processes through model selection methods. However, identifying corresponding nonlinear systems for different physical phenomena using numerical methods can be computationally prohibitive. With the advent of machine learning (ML) algorithms, more efficient surrogate models based on neural networks (NNs) have been developed in various disciplines. In this work, a theory-guided U-net (TgU-net) framework is proposed for surrogate modeling of three-dimensional (3D) groundwater contaminant problems in order to efficiently elucidate their involved processes and unknown parameters. In TgU-net, the underlying governing equations are embedded into the loss function of U-net as soft constraints. For the considered groundwater contaminant problem, sorption is considered to be a potential process of an uncertain type, and three equilibrium sorption isotherm types (i.e., linear, Freundlich, and Langmuir) are considered. Different from traditional approaches in which one model corresponds to one equation, these three sorption types are modeled through only one TgU-net surrogate. The three mentioned sorption terms are integrated into one equation by assigning indicators. Accurate predictions illustrate the satisfactory generalizability and extrapolability of the constructed TgU-net. Furthermore, based on the constructed TgU-net surrogate, a data assimilation method is employed to identify the physical process and parameters simultaneously. This work shows the possibility of governing equation discovery of physical problems that contain multiple and even uncertain processes by using deep learning and data assimilation methods.