| 03 Feb 2026
Ensemble Kalman–Guided Model Predictive Path Integral Control for Spatially Localized Suppression of Extremes in Chaotic Geophysical Flows
Abstract. The possibility of influencing extreme weather phenomena has been discussed for decades; however, it remains far from operational practice, and there is still no established framework for designing small, spatially localized perturbations that can reliably steer chaotic geophysical flows. In this study, we propose a hybrid control method, termed ensemble-Kalmanguided model predictive path integral control (EKG-MPPI), which combines ensemble Kalman control (EnKC) with model predictive path integral (MPPI) control. Within a control simulation experiment framework, an ensemble Kalman filter is first used for state estimation, after which EnKC computes a candidate perturbation by treating the control objective as a pseudo-observation. An adaptive thresholding procedure then enforces spatial sparsity, so that the EnKC perturbation identifies candidate actuator locations and their nominal amplitudes. This information is embedded into the mean and covariance of Gaussian proposal distributions for MPPI, which subsequently refines the perturbation through sampling-based optimization with nonlinear rollouts, without linearizing the dynamics or computing gradients. Numerical experiments with the Lorenz–96 model and the surface quasi-geostrophic (SQG) model demonstrate that EKG-MPPI can suppress extremes in state variables and regional wind speed more effectively than EnKC alone, while using comparable or smaller control inputs. These results highlight EKG-MPPI as a promising building block for simulation-based assessment of localized intervention strategies in geophysical flows.
This manuscript presents a novel and elegant hybrid control strategy, termed EKG-MPPI, aimed at spatially localized interventions in chaotic geophysical flows. By combining the statistical data assimilation capabilities of Ensemble Kalman Control (EnKC) with the nonlinear, derivative-free optimization of Model Predictive Path Integral (MPPI) control, the authors provide a compelling framework for "Control Simulation Experiments". From a systems and control engineering perspective, using the EnKC to generate a sparse, physics-informed prior to guide the sampling distribution of the MPPI is a brilliant approach to solving the sample inefficiency inherent to high-dimensional state spaces. The method is entirely matrix-free and avoids the computation of adjoint models or gradients, which is highly desirable for chaotic, non-linear atmospheric models. However, while the theoretical hybridization is sound, the current implementation simplifies the temporal complexity of the control problem to a single-step actuation. This reduces the framework to a static spatial optimization problem rather than true multi-step trajectory optimization. Furthermore, the comparison with baseline methods lacks rigorous hyperparameter tuning, which somewhat weakens the performance claims. The manuscript is a strong proof-of-concept, but addressing the specific points below would significantly improve its rigor and impact.
Specific Comments :
- Single-Step Actuation vs. Sequential Trajectory Optimization: The authors explicitly state that the control perturbation is applied only at the first rollout step, with no further input provided during the remaining prediction horizon ($T_{MPPI}$). Because the problem is reduced to optimizing a single initial impulse, the use of MPP, a method designed for sequential, multi-step trajectory optimization, seems algorithmically oversized. The authors should discuss why MPPI was chosen over standard derivative-free black-box optimization algorithms (e.g., CMA-ES or Bayesian Optimization) which are highly efficient for static, single-step parameter search. If the intention is to lay the groundwork for future multi-step actuation, this should be stated more explicitly as the primary justification for using the MPPI formalism.
- Fairness in Baseline Comparison (Hyperparameter Optimization): In Section 4.1.1, the proposed EKG-MPPI is compared against a "vanilla MPPI" baseline. However, the setup for the vanilla MPPI utilizes arbitrarily fixed hyperparameters without any apparent tuning. Specifically, the authors set the temperature parameter to $\lambda = 0.7$ for the vanilla MPPI, whereas EKG-MPPI operates with $\lambda = 0.1$. Furthermore, the vanilla MPPI relies on a completely static sampling distribution (variance of 0.5 for magnitude and 20.0 for location). Because EKG-MPPI inherently adapts both the mean and variance of its sampling distribution using the EnKC output, it naturally possesses a massive advantage. To ensure a rigorous comparative analysis, the baseline MPPI should ideally undergo a degree of hyperparameter tuning or at least a sensitivity analysis similar to the one performed for EKG-MPPI in Figure 3 to firmly demonstrate that its poorer performance is due to the lack of EnKC guidance rather than sub-optimal static parameters.
- Computational Scalability and Profiling: The results in Table 2 show that EKG-MPPI is the most computationally expensive method tested. While the authors correctly point out that MPPI rollouts are "embarrassingly parallel" and benefit directly from GPU acceleration, a brief computational profiling of the EKG-MPPI execution time would be highly valuable. Specifically, providing a breakdown of the time spent computing the EnKC prior versus the time spent evaluating the MPPI rollouts would clarify where the true bottleneck lies. Given the authors' stated intention in the conclusion to scale this approach to multi-actuator and multi-step scenarios, this profiling would help readers assess the operational feasibility of scaling the framework.
Technical Corrections :
- Equation notations: In Section 3.2, Step 3, the embedding functions $f_{loc}$, $g_{loc}$, $f_{mag}$, and $g_{mag}$ are introduced. It would be helpful to the reader to add a brief sentence clarifying their exact mathematical definitions or references earlier in the text, before they are fully explicitly defined for the experiments in Equations (39) and (50).