Data assimilation using sequential monte carlo methods in wildfire spread simulation

Data assimilation is the process of estimating the state of dynamic systems (linear or nonlinear, Gaussian or non-Gaussian) as accurately as possible from noisy observational data. Although the Three Dimensional Variational (3D-VAR) methods, Four Dimensional Variational (4D-VAR) methods and Ensemble Kalman filter (EnKF) methods are widely used and effective for linear and Gaussian dynamics, new methods of data assimilation are required for the general situation, that is, nonlinear non-Gaussian dynamics. General Bayesian recursive estimation theory is reviewed in this thesis. The Bayesian estimation approach provides a rather general and powerful framework for handling nonlinear, non-Gaussian, as well as linear, Gaussian estimation problems. Despite a general solution to the nonlinear estimation problem, there is no closed-form solution in the general case. Therefore, approximate techniques have to be employed. In this thesis, the sequential Monte Carlo (SMC) methods, commonly referred to as the particle filter, is presented to tackle non-linear, non-Gaussian estimation problems. In this thesis, we use the SMC methods only for the nonlinear state estimation problem, however, it can also be used for the nonlinear parameter estimation problem. In order to demonstrate the new methods in the general nonlinear non-Gaussian case, we compare Sequential Monte Carlo (SMC) methods with the Ensemble Kalman Filter (EnKF) by performing data assimilation in nonlinear and non-Gaussian dynamic systems. The models used in this study are referred to as state-space models. The Lorenz 1963 and 1966 models serve as test beds for examining the properties of these assimilation methods when used in highly nonlinear dynamics. The application of Sequential Monte Carlo methods to different fixed parameters in dynamic models is considered. Four different scenarios in the Lorenz 1063 [sic] model and three different scenarios in the Lorenz 1996 model are designed in this study for both the SMC methods and EnKF method with different filter siz

Data assimilation is a method to improve the state inference by assimilating the real time observation data into the systems under study. In wildfire spread simulation, the deployed fire sensors are used to collect the real time temperatures, which can be infused into the wildfire spread simulation model for improved state predictions. However, for many scenarios, the temperature data is limited due to the unavailability of the deployed sensors. With the rapid development of social networking, many other types of data, such as the geo-referenced images, can be obtained from the public websites. In this paper, we propose the data assimilation method to assimilate the geo-referenced images into the wildfire spread simulation using sequential Monte Carlo (SMC) methods. We will show its effectiveness to improve the state estimation by the proposed data assimilation method through the designed experiments.

This article develops a spatial partition-based particle filtering framework to support data assimilation for large-scale wildfire spread simulation effectively. The developed spatial partition-based particle filtering framework breaks the system state and observation data into smaller spatial regions and then carries out localized particle filtering based on these spatial regions. Particle Filters (PFs) hold great promise to support data assimilation for spatial temporal simulations, such as wildfire spread simulation, to achieve more accurate simulation or prediction results. However, PFs face major challenges to work effectively for complex spatial temporal simulations due to the high-dimensional state space of the simulation models, which typically cover large areas and have a large number of spatially dependent state variables. The developed framework exploits the spatial locality property of system state and observation data and employs the divide-and-conquer principle to reduce state dimension and data complexity. This framework is especially developed for a discrete event cellular space model (the wildfire simulation model), which significantly differs from prior works that use numerical models specified by partial differential equations (PDEs) with continuous variables. Within this framework, a two-level automated spatial partitioning method is presented to provide automated and balanced spatial partitions with fewer boundary sensors. The developed framework is applied to a wildfire spread simulation and achieved improved results compared to using standard PF-based data assimilation methods.

The regular and repetitive nature of the sequential Monte Carlo (SMC) method makes it very attractive for implementation using parallel and pipelined architectures. This paper develops a VLSI architecture for the hardware implementation of the SMC algorithm using bootstrap filter. A flat fading wireless channel is considered as our framework on which the channel estimator is designed and implemented using the SMC method. The design and verification activities at the algorithm level, architecture level, and the circuit level are reviewed. The proposed architecture is verified with an FPGA implementation.

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We prove finite sample concentration bounds for estimators derived from the proposed method along with a linear tempering extension and apply these results to a realistic setting where a computer model is misspecified. We then illustrate the SMC method for inference in a modular chemical reactor example that includes submodels for reaction kinetics, turbulence, mass transfer, and diffusion. The samples obtained are commensurate with a direct-sampling approach that consists of running multiple Markov chains, with computational efficiency gains using the SMC method. Overall, the SMC method presented yields a novel, rigorous approach to computing with cut-Bayesian posterior distributions.

Online Estimation of DSGE Models

In several implementations of Sequential Monte Carlo (SMC) methods it is natural and important, in terms of algorithmic efficiency, to exploit the information of the history of the samples to optimally tune their subsequent propagations. In this article we provide a carefully formulated asymptotic theory for a class of such adaptive SMC methods. The theoretical framework developed here will cover, under assumptions, several commonly used SMC algorithms [Chopin, Biometrika 89 (2002) 539-551; Jasra et al., Scand. J. Stat. 38 (2011) 1-22; Schafer and Chopin, Stat. Comput. 23 (2013) 163- 184]. There are only limited results about the theoretical underpinning of such adaptive methods: We will bridge this gap by providing a weak law of large numbers (WLLN) and a central limit theorem (CLT) for some of these algorithms. The latter seems to be the first result of its kind in the literature and provides a formal justification of algorithms used in many real data contexts [Jasra et al. (2011); Schafer and Chopin (2013)]. We establish that for a general class of adaptive SMC algorithms [Chopin (2002)], the asymptotic variance of the estimators from the adaptive SMC method is identical to a limiting SMC algorithm which uses ideal proposal kernels. Our results are supported by application on a complex high-dimensional posterior distribution associated with the Navier-Stokes model, where adapting highdimensional parameters of the proposal kernels is critical for the efficiency of the algorithm.

A coherent structure approach for parameter estimation in Lagrangian Data Assimilation

Wildfire propagation is a complex process influenced by many factors. Simulation models of wildfire spread, such as DEVS-FIRE, are important tools for studying fire behavior. This paper presents how the sequential Monte Carlo methods, i.e., particle filters, can work together with DEVS-FIRE for better simulation and prediction of wildfire. We define an application framework of particle filters for the problem of wildfire spread using the DEVS-FIRE model, and discuss several applications. A case study example is provided and preliminary results are presented.

We develop novel approaches to enhance the functionality and efficiency of digital twins through deep learning techniques. Digital twins, sophisticated virtual models of physical systems, serve as dynamic counterparts, mirroring real-world entities' behavior and performance. Their primary role includes real-time monitoring, flaw detection, automated control, and proactive maintenance. To perform such tasks it is necessary to use various methods from scientific computing to combine data with physics models. Furthermore, to assess the reliability of a digital twin, it is important to not only make predictions, but also quantify the uncertainty of estimations and predictions. In this regard, Bayesian methods serve as a natural framework to pose the problems. However, the complexity and real-time operation requirements pose significant computational challenges. The thesis explores the integration of deep learning in scientific computing for enabling digital twins. The focus is on overcoming the computational hurdles in real-time data assimilation and inverse problem-solving through surrogate modeling. Deep learning, with its capability to handle high-dimensional functions in both deterministic and stochastic settings is shown to be a viable solution to these challenges. This work investigates several key areas, beginning with a brief introduction to digital twins, data assimilation, and inverse problems. It proceeds to elaborate on the role of Bayesian inversion problems in static and dynamic contexts, highlighting the importance of uncertainty quantification. The focus is on the challenges of real-time computation and the potential of Bayesian methods, despite their computational intensity. The thesis investigates deep learning architectures like dense and residual neural networks, convolutional neural networks, recurrent neural networks and transformers. The core contributions are presented in the four main chapters of the thesis: 1) Reduced Order Modeling for Parameterized Time-Dependent Partial Differential Equations: Introducing a deep learning framework for solving parameterized PDEs using spatially and memory-aware neural networks, demonstrated on linear advection and incompressible Navier-Stokes equations. 2) Markov Chain Generative Adversarial Neural Networks: Enhancing Bayesian inversion for static problems with sparse observations using a unique algorithm combining MCMC and GANs, demonstrated on a Darcy flow problem and pipe flow leakage detection. 3) Probabilistic Digital Twin for Leak Localization: Developing a probabilistic framework using supervised Wasserstein Autoencoders for leak localization in water distribution networks, tested on several network models. 4) The Deep Latent Space Particle Filter: Proposing a real-time nonlinear data assimilation method for dynamic PDEs with uncertainty quantification, using transformer-based dimensionality reduction and time-stepping in particle filters, demonstrated on various dynamic systems. This thesis contributes significantly to digital twins, addressing computational limitations and opening new avenues for practical applications in various industries.

We consider estimating a stochastic intensity process, indirectly observed through a sequence of Poisson random variables. The class of dynamical systems we consider, are autoregressive state processes and a sequence of Poisson distributed observations, each influenced by the state process. Computing explicit recursive filters for this class of system can be technically difficult. Further, exact filters for this class of model do not have fixed memory requirements. It is shown in Manton et al. (1999), that the exact filter for these models has linear growth with respect to time in the number of sufficient statistics needed to construct the filter density. Some approximate suboptimal filters are available for these models using Edgeworth expansions. Using Sequential Monte Carlo (SMC) methods and the so called Bayesian bootstrap filter, we propose a scheme to estimate an intensity process for the models just described. The scheme we present is simple to implement and has fixed memory requirements. A simulation study is included to demonstrate the performance of SMC methods for discrete time models with Poisson observations.

Intractable sequential inference arises in several applications in the physical engineering process. One of the most successful and efficient stochastic simulation techniques that is appropriate to perform the Bayesian inference (inversion decision) in complex dynamic models is the sequential Monte Carlo (SMC) methods. Although, these methods have become widely accepted among researchers and practitioners, in practice the manifestation of the path degeneracy implies a poor approximation of the target measures. This is an unavoidable deep problem when approximating sequence target models, and it becomes evident when strong non-linearity is presented. To deal with this drawback of the SMC methods, a promise mechanism is used to create particle diversity to move the particle according some kernel perturbation. In this article, we apply in three non-linear engineering dynamical systems (reservoir dynamics, van de Vusse reaction and pipe-in-pipe), a class of move algorithms, without the need to change the computational complexity called the move-regweighting scheme proposed by Marques and Storvik [(Particle move-reweighting strategies for online inference. Preprint series. Statistical Research Report (1), 2013]. Numerical simulations with different number of particles are performed to demonstrate the accuracy of the algorithm.

In statistical signal processing, the sequential Monte Carlo (SMC) method is powerful and can approach the theoretical optima. However, its computational complexity is usually very high, especially in multiple-input multiple-output (MIMO) systems. This paper presents a new low-complexity SMC (LC-SMC) algorithm for blind detection in MIMO systems, the main idea of which is to shrink the sampling space via channel estimation which is initialized using the first differentially modulated symbol and then updated using the Monte Carlo samples. Since the a posteriori probability of the transmitted symbols can be calculated separately by each transmit antenna, the proposed LC-SMC algorithm is not only computationally efficient, as compared to the original SMC whose complexity grows exponentially with the number of transmit antennas, but also makes blind turbo receiver more feasible for multilevel/phase modulations. Simulation results are presented to demonstrate the effectiveness of the LC-SMC algorithm

International audience

<p>Assimilating surface soil moisture data or GRACE data, retrieved from satellite, into hydrological models has been proven to improve the accuracy of hydrological model estimations and predictions. For data assimilation applications in hydrology, the ensemble Kalm filter(EnKF) is the most commonly used data assimilation(DA) method. Particle filters are a type of non-Gaussian filter that doesn’t need the normality assumption that the EnKF needs. Adding localization defeats the curse of dimensionality that is a problem in normal particle filters. In the present study, we investigated our adaption of the local particle filter based on the Gamma test theory(LPF-GT) to improve discharge estimates by assimilating SMAP satellite soil moisture into the PCR-GLOBWB hydrological model. The study area is the Rhine river basin, driven by forcing data from April 2015 to December 2016. The improved discharge estimates are obtained by using DA to adjust the surface soil moisture in the model. The influence of DA to discharge is not direct but works through the dynamics of the hydrological model.  To explore the potential of LPF-GT, serval sensitivity experiments were conducted to figure out the impact of localization scales and the number of particles on DA's performance. The DA estimates were validated against in situ discharge measurements from gauge stations. To demonstrate the benefit of LPF-GT, EnKF was used as a benchmark in this research. Increases in Nash-Sutcliffe (0.05%– 38%) and decreases in normalized RMSE (0.02%–3.4%) validated the capability of LPF-GT. Results showed that localization scales' impact was substantial. The optimal value of the localization scale was obtained by tuning. LPF-GT achieved a satisfactory performance when only using a few particles, even with as little as five particles. The sample errors posed an adverse impact on the open-loop results. Further improvement could be achieved by considering reduce sample errors due to a small number of particles.</p>