More Like this

1. An Evaluation of Non-Gaussian Data Assimilation Methods in Moist Convective Regimes

   https://doi.org/10.1175/MWR-D-22-0260.1  

   McCurry, Joshua; Poterjoy, Jonathan; Knopfmeier, Kent; Wicker, Louis (July 2023, Monthly Weather Review)

   Abstract Obtaining a faithful probabilistic depiction of moist convection is complicated by unknown errors in subgrid-scale physical parameterization schemes, invalid assumptions made by data assimilation (DA) techniques, and high system dimensionality. As an initial step toward untangling sources of uncertainty in convective weather regimes, we evaluate a novel Bayesian data assimilation methodology based on particle filtering within a WRF ensemble analysis and forecasting system. Unlike most geophysical DA methods, the particle filter (PF) represents prior and posterior error distributions nonparametrically rather than assuming a Gaussian distribution and can accept any type of likelihood function. This approach is known to reduce bias introduced by Gaussian approximations in low-dimensional and idealized contexts. The form of PF used in this research adopts a dimension-reduction strategy, making it affordable for typical weather applications. The present study examines posterior ensemble members and forecasts for select severe weather events between 2019 and 2020, comparing results from the PF with those from an ensemble Kalman filter (EnKF). We find that assimilating with a PF produces posterior quantities for microphysical variables that are more consistent with model climatology than comparable quantities from an EnKF, which we attribute to a reduction in DA bias. These differences are significant enough to impact the dynamic evolution of convective systems via cold pool strength and propagation, with impacts to forecast verification scores depending on the particular microphysics scheme. Our findings have broad implications for future approaches to the selection of physical parameterization schemes and parameter estimation within preexisting data assimilation frameworks. Significance StatementThe accurate prediction of severe storms using numerical weather models depends on effective parameterization schemes for small-scale processes and the assimilation of incomplete observational data in a manner that faithfully represents the probabilistic state of the atmosphere. Current generation methods for data assimilation typically assume a standard form for the error distributions of relevant quantities, which can introduce bias that not only hinders numerical prediction, but that can also confound the characterization of errors from the model itself. The current study performs data assimilation using a novel method that does not make such assumptions and explores characteristics of resulting model fields and forecasts that might make such a method useful for improving model parameterization schemes. 

   more » « less
2. A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation

   https://doi.org/10.3934/fods.2021019  

   Maclean, John; Spiller, Elaine T. (January 2021, Foundations of Data Science)

   null (Ed.)

   Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary strategy that combines statistical emulators and particle filters. The emulators are used to learn and offer a computationally cheap approximation to the forward dynamic mapping. This emulator-particle filter (Emu-PF) approach requires a modest number of forward-model runs, but yields well-resolved posterior distributions even in non-Gaussian cases. We explore several modifications to the Emu-PF that utilize mechanisms for dimension reduction to efficiently fit the statistical emulator, and present a series of simulation experiments on an atypical Lorenz-96 system to demonstrate their performance. We conclude with a discussion on how the Emu-PF can be paired with modern particle filtering algorithms. 

   more » « less
3. Physically Invertible System Identification for Monitoring System Edges with Unobservability

   Jingyi Yuan and Yang Weng (September 2022, Machine Learning and Knowledge Discovery in Databases: European Conference)

   Nowadays, the data collected in physical/engineering systems allows various machine learning methods to conduct system monitoring and control, when the physical knowledge on the system edge is limited and challenging to recover completely. Solving such problems typically requires identifying forward system mapping rules, from system states to the output measurements. However, the forward system identification based on digital twin can hardly provide complete monitoring functions, such as state estimation, e.g., to infer the states from measurements. While one can directly learn the inverse mapping rule, it is more desirable to re-utilize the forward digital twin since it is relatively easy to embed physical law there to regularize the inverse process and avoid overfitting. For this purpose, this paper proposes an invertible learning structure based on designing parallel paths in structural neural networks with basis functionals and embedding virtual storage variables for information preservation. For such a two-way digital twin modeling, there is an additional challenge of multiple solutions for system inverse, which contradict the reality of one feasible solution for the current system. To avoid ambiguous inverse, the proposed model maximizes the physical likelihood to contract the original solution space, leading to the unique system operation status of interest. We validate the proposed method on various physical system monitoring tasks and scenarios, such as inverse kinematics problems, power system state estimation, etc. Furthermore, by building a perfect match of a forward-inverse pair, the proposed method obtains accurate and computation-efficient inverse predictions, given observations. Finally, the forward physical interpretation and small prediction errors guarantee the explainability of the invertible structure, compared to standard learning methods. 

   more » « less
4. Efficient derivative-free Bayesian inference for large-scale inverse problems

   https://doi.org/10.1088/1361-6420/ac99fa  

   Huang, Daniel Zhengyu; Huang, Jiaoyang; Reich, Sebastian; Stuart, Andrew M (October 2022, Inverse Problems)

   Abstract We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O ( 1 0 4 ) model runs, or more. Moreover, the forward model is often given as a black box or is impractical to differentiate. Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems. The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system, into which the inverse problem is embedded as an observation operator. Theoretical properties are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it. This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior. Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model; and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach. The effectiveness of the framework is demonstrated in several numerical experiments, including proof-of-concept linear/nonlinear examples and two large-scale applications: learning of permeability parameters in subsurface flow; and learning subgrid-scale parameters in a global climate model. Moreover, the stochastic ensemble Kalman filter and various ensemble square-root Kalman filters are all employed and are compared numerically. The results demonstrate that the proposed method, based on exponential convergence to the filtering distribution of a mean-field dynamical system, is competitive with pre-existing Kalman-based methods for inverse problems. 

   more » « less
5. Modeling surface pH measurements of oocytes

   https://doi.org/10.1088/2057-1976/ac71d0  

   Bocchinfuso, A; Calvetti, D; Somersalo, E (June 2022, Biomedical Physics & Engineering Express)

   Abstract The transport of gases across cell membranes plays a key role in many different cell functions, from cell respiration to pH control. Mathematical models play a central role in understanding the factors affecting gas transport through membranes, and are the tool needed for testing the novel hypothesis of the preferential crossing through specific gas channels. Since the surface pH of cell membrane is regulated by the transport of gases such as CO 2 and NH 3 , inferring the membrane properties can be done indirectly from pH measurements. Numerical simulations based on recent models of the surface pH support the hypothesis that the presence of a measurement device, a liquid-membrane pH sensitive electrode on the cell surface may disturb locally the pH, leading to a systematic bias in the measured values. To take this phenomenon into account, it is necessary to equip the model with a description of the micro-environment created by the pH electrode. In this work we propose a novel, computationally lightweight numerical algorithm to simulate the surface pH data. The effect of different parameters of the model on the output are investigated through a series of numerical experiments with a physical interpretation. 

   more » « less