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WP4: Inverse Problems and Data Assimilation
WP4 combines data and models by formulating and solving inverse problems using deterministic and stochastic methods, with multi-fidelity modeling for exascale efficiency.
Recent Highlights (2024-2025)
Time-Parallel 4D-Var
Weak-constraint 4D-Var methods for time-parallel data assimilation
Ensemble Methods
Ensemble-based approaches for error covariance estimation
Multi-Fidelity Strategies
Multi-fidelity strategies for inverse problems at scale
Hybrid Methods
Hybrid ensemble-variational methods with improved scalability
1. Objectives
The combination of data and models is achieved through inverse problems, covering:
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Deterministic and stochastic models and methods
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Observation sparsity and sufficiency considerations
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Multi-fidelity models (MFM) including reduced-order and AI-based surrogates
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Scaling of inverse problem solution methods to exascale
3. Key Tasks
T4.1: Deterministic Methods
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Time-parallel methods with weak-constraint formulation of variational assimilation
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Exploit different physics, spatial and temporal scales for improved parallelism
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Develop hybrid ensemble-variational approaches using ensembles for better error covariance
T4.2: Stochastic Methods
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Implement stochastic processes obeying stochastic differential equations (SDEs)
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First approach: Itô theory with stochastic ordinary differential equations
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Second approach: Stochastic partial differential equations (SPDE)
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Study and compare approaches on classical inverse and data assimilation problems
T4.3: Observations
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Improve description of observation error statistics beyond uncorrelated Gaussian errors
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Address forecast errors dominated by position errors
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Develop alternative metrics based on transport theory
T4.4: Multi-Fidelity Modeling
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Joint work with WP2, Task T2.5
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Consider PINN-type models as candidates for multi-fidelity models
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Integration with WP2 Tasks T2.1 and T2.2 (neural operators)
T4.5: Model Management and Scheduling
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Develop model management/scheduling strategies
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Combine high-fidelity and lower-fidelity models optimally
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Minimize variance in stochastic frameworks
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Focus on exascale scaling as central issue
5. Addressed Exascale Bottlenecks
WP4 targets bottlenecks B8 (Discovery, design, and decision algorithms) and B13 (Opportunity to integrate uncertainties):
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Enabling ensembles of many small runs for data assimilation
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Combining data and models through inverse problems
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Integrating uncertainties directly into calculations
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Efficient use of parallel resources for ensemble methods