Jointly Learning Dynamics and Data Assimilation from Sparse Observations using End-to-End Deep Learning

核心概念

A novel end-to-end deep learning framework, CODA, that jointly learns dynamical models and performs data assimilation directly from sparse and noisy observations, without requiring access to ground truth system states.

摘要

The paper introduces a novel deep learning-based framework called CODA (Combined Optimization of Dynamics and Assimilation) for solving inverse problems in geoscience applications. CODA jointly learns a neural network for data assimilation (DA) and tunes parameters of a dynamical model, all from sparse and noisy observations, without requiring access to ground truth system states.

Key highlights:

• CODA trains a neural network to perform parallel-in-time DA, using a loss function that combines data consistency and model self-consistency terms.
• The DA network and dynamical model parameters are optimized jointly in an end-to-end fashion, breaking the "chicken-and-egg" problem between accurate models and accurate state estimates.
• CODA is demonstrated on the Lorenz'96 system, showing it can effectively perform DA, parameter tuning, and learning corrective terms for unresolved processes, outperforming classical DA methods.
• The parallel-in-time nature and differentiability of CODA enable robust and efficient optimization, even in the presence of model misspecification.

The paper presents a principled and flexible framework for integrating machine learning with physical models, opening up new possibilities for data-driven discovery and forecasting in the geosciences.

统计

The Lorenz'96 system has 40 state variables and a forcing parameter F that controls the system's chaotic behavior.
Observations are generated with 75% missing values and Gaussian noise with standard deviation of 1.0.
The RMSE between the CODA analysis and ground truth simulation is less than half the observation noise, even with up to 95% missing data and noise standard deviation of 3.0.
For parameter tuning, the randomly initialized estimate of the forcing parameter F converges close to the true value over gradient steps.
The learned corrective term for unresolved fine-scale variables in the two-level Lorenz'96 system closely matches the true coupling term, improving the accuracy of both data assimilation and free-running simulations.

引用

"Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this deadlock we present CODA, an end-to-end optimization scheme for jointly learning dynamics and DA directly from sparse and noisy observations."
"By taking into account interactions between new and existing simulation components over multiple time steps, CODA can recover initial conditions, fit unknown dynamical parameters and learn neural network-based PDE terms to match both available observations and self-consistency constraints."
"In addition to facilitating end-to-end learning of dynamics and providing fast, amortized, non-sequential DA, CODA provides greater robustness to model misspecification than classical DA approaches."

从中提取的关键见解

Combined Optimization of Dynamics and Assimilation with End-to-End Learning on Sparse Observations

by Vadim Zinche... 在 arxiv.org 09-12-2024

https://arxiv.org/pdf/2409.07137.pdf

更深入的查询

How could the CODA framework be extended to handle higher-dimensional and more complex geophysical models, such as those used in weather and climate prediction?

The CODA (Combined Optimization of Dynamics and Assimilation) framework can be extended to higher-dimensional and more complex geophysical models by leveraging its inherent flexibility and differentiability. Here are several strategies for this extension:

Multi-scale Modeling: Higher-dimensional models often involve multiple spatial and temporal scales. CODA can be adapted to incorporate multi-scale dynamics by integrating hierarchical neural networks that can learn both coarse and fine-scale processes. This would allow the framework to effectively parameterize unresolved scales while maintaining the ability to assimilate data across different resolutions.

Advanced Neural Network Architectures: Utilizing more sophisticated neural network architectures, such as 3D convolutional networks or recurrent neural networks (RNNs), can enhance the CODA framework's ability to process and learn from high-dimensional data. These architectures can capture spatial and temporal dependencies more effectively, which is crucial for complex geophysical processes.

Incorporation of Physical Constraints: To ensure that the learned dynamics remain physically plausible, the CODA framework can integrate physical constraints directly into the loss function. This could involve using conservation laws or other domain-specific knowledge to guide the learning process, thereby improving the robustness of the model against misspecification.

Parallelization and Distributed Computing: Given the computational demands of higher-dimensional models, extending CODA to utilize parallel computing and distributed architectures can significantly enhance its scalability. This would allow for simultaneous processing of multiple data assimilation tasks, improving efficiency and reducing computation time.

Adaptive Observation Strategies: Implementing adaptive observation strategies that prioritize data collection in regions of high uncertainty or dynamic change can improve the effectiveness of CODA in complex models. This would involve dynamically adjusting the assimilation window and observation operators based on real-time model performance.

What are the potential challenges in scaling CODA to large-scale Earth system models, and how could they be addressed?

Scaling the CODA framework to large-scale Earth system models presents several challenges, including:

Computational Complexity: Large-scale models often involve high-dimensional state spaces and complex dynamics, leading to significant computational demands. To address this, CODA can be optimized through techniques such as model reduction, where less critical dynamics are simplified or omitted, and by employing efficient numerical methods for integration and optimization.

Data Volume and Quality: The volume of observational data in large-scale models can be overwhelming, especially when dealing with sparse and noisy observations. Implementing robust data preprocessing techniques, such as outlier detection and noise reduction algorithms, can enhance data quality before assimilation. Additionally, using dimensionality reduction techniques like Principal Component Analysis (PCA) can help manage the data volume.

Memory Constraints: The memory requirements for storing high-dimensional state variables and their gradients can be prohibitive. Utilizing memory-efficient data structures and algorithms, such as mini-batch processing and gradient checkpointing, can mitigate these constraints. Furthermore, leveraging cloud computing resources can provide the necessary infrastructure for handling large datasets.

Model Misspecification: Large-scale models are often subject to significant uncertainties and misspecifications. To counter this, CODA can incorporate uncertainty quantification methods, allowing for the estimation of confidence intervals around predictions and the identification of model deficiencies. This could involve ensemble methods that generate multiple model realizations to capture the range of possible outcomes.

Integration with Existing Frameworks: Large-scale Earth system models often rely on established frameworks and software. Ensuring that CODA can be seamlessly integrated with these existing systems is crucial. This may involve developing APIs or modular components that allow CODA to interface with other modeling tools, facilitating a more cohesive modeling environment.

Could the CODA approach be adapted to incorporate uncertainty quantification and ensemble-based methods, in addition to point estimates of parameters and states?

Yes, the CODA approach can be effectively adapted to incorporate uncertainty quantification and ensemble-based methods alongside point estimates of parameters and states. Here are several ways to achieve this:

Ensemble Kalman Filtering (EnKF): By integrating ensemble-based methods like the Ensemble Kalman Filter into the CODA framework, it can leverage multiple model realizations to account for uncertainties in both the model dynamics and the observational data. This would allow CODA to produce probabilistic forecasts and uncertainty estimates, enhancing its robustness in the face of model misspecification.

Bayesian Inference: Adapting CODA to utilize Bayesian inference techniques can facilitate the incorporation of prior knowledge and uncertainty quantification. By treating model parameters and states as random variables with associated probability distributions, CODA can update these distributions based on incoming observational data, providing a comprehensive view of uncertainty.

Stochastic Modeling: Introducing stochastic elements into the CODA framework can help capture the inherent uncertainties in geophysical processes. This could involve modeling the dynamics with stochastic differential equations (SDEs) or incorporating noise terms directly into the neural network architecture, allowing for a more realistic representation of uncertainty.

Multi-fidelity Approaches: CODA can be extended to utilize multi-fidelity modeling, where different levels of model complexity are employed based on the available data and computational resources. This approach allows for the efficient exploration of parameter space and uncertainty quantification by combining high-fidelity models with lower-fidelity approximations.

Uncertainty Propagation: Implementing methods for uncertainty propagation within the CODA framework can help track how uncertainties in initial conditions and parameters affect model outputs. Techniques such as Monte Carlo simulations or polynomial chaos expansions can be employed to quantify the impact of uncertainties on predictions, providing valuable insights into model reliability.

By incorporating these strategies, the CODA framework can enhance its capability to handle uncertainties, making it a more powerful tool for data assimilation and model calibration in complex geophysical systems.