Dan Pagendam

Joel Janek Dabrowski, Daniel Edward Pagendam, James Hilton et al.

We apply the Physics Informed Neural Network (PINN) to the problem of wildfire fire-front modelling. We use the PINN to solve the level-set equation, which is a partial differential equation that models a fire-front through the zero-level-set of a level-set function. The result is a PINN that simulates a fire-front as it propagates through the spatio-temporal domain. We show that popular optimisation cost functions used in the literature can result in PINNs that fail to maintain temporal continuity in modelled fire-fronts when there are extreme changes in exogenous forcing variables such as wind direction. We thus propose novel additions to the optimisation cost function that improves temporal continuity under these extreme changes. Furthermore, we develop an approach to perform data assimilation within the PINN such that the PINN predictions are drawn towards observations of the fire-front. Finally, we incorporate our novel approaches into a Bayesian PINN (B-PINN) to provide uncertainty quantification in the fire-front predictions. This is significant as the standard solver, the level-set method, does not naturally offer the capability for data assimilation and uncertainty quantification. Our results show that, with our novel approaches, the B-PINN can produce accurate predictions with high quality uncertainty quantification on real-world data.

Zhibin Li, Piotr Koniusz, Lu Zhang et al.

Traditional approaches for learning on categorical data underexploit the dependencies between columns (\aka fields) in a dataset because they rely on the embedding of data points driven alone by the classification/regression loss. In contrast, we propose a novel method for learning on categorical data with the goal of exploiting dependencies between fields. Instead of modelling statistics of features globally (i.e., by the covariance matrix of features), we learn a global field dependency matrix that captures dependencies between fields and then we refine the global field dependency matrix at the instance-wise level with different weights (so-called local dependency modelling) w.r.t. each field to improve the modelling of the field dependencies. Our algorithm exploits the meta-learning paradigm, i.e., the dependency matrices are refined in the inner loop of the meta-learning algorithm without the use of labels, whereas the outer loop intertwines the updates of the embedding matrix (the matrix performing projection) and global dependency matrix in a supervised fashion (with the use of labels). Our method is simple yet it outperforms several state-of-the-art methods on six popular dataset benchmarks. Detailed ablation studies provide additional insights into our method.

Joel Janek Dabrowski, Daniel Edward Pagendam

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than Variational Inference, and it does not rely on adversarial training (or density ratio estimation). We adopt the recent approach of constructing two models: (1) a primary model, tasked with performing regression or classification; and (2) a secondary, expressive (e.g. implicit) model that defines an approximate posterior distribution over the parameters of the primary model. However, we optimise the parameters of the posterior model via gradient descent according to a Monte Carlo estimate of the posterior predictive distribution -- which is our only approximation (other than the posterior model). Only a likelihood needs to be specified, which can take various forms such as loss functions and synthetic likelihoods, thus providing a form of a likelihood-free approach. Furthermore, we formulate the approach such that the posterior samples can either be independent of, or conditionally dependent upon the inputs to the primary model. The latter approach is shown to be capable of increasing the apparent complexity of the primary model. We see this being useful in applications such as surrogate and physics-based models. To promote how the Bayesian paradigm offers more than just uncertainty quantification, we demonstrate: uncertainty quantification, multi-modality, as well as an application with a recent deep forecasting neural network architecture.

Dan MacKinlay, Russell Tsuchida, Dan Pagendam et al.

Efficient inference in high-dimensional models is a central challenge in machine learning. We introduce the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, which combines the strengths of the Ensemble Kalman Filter (EnKF) and Gaussian Belief Propagation (GaBP) to address this challenge. GEnBP updates ensembles of prior samples into posterior samples by passing low-rank local messages over the edges of a graphical model, enabling efficient handling of high-dimensional states, parameters, and complex, noisy, black-box generation processes. By utilizing local message passing within a graphical model structure, GEnBP effectively manages complex dependency structures and remains computationally efficient even when the ensemble size is much smaller than the inference dimension -- a common scenario in spatiotemporal modeling, image processing, and physical model inversion. We demonstrate that GEnBP can be applied to various problem structures, including data assimilation, system identification, and hierarchical models, and show through experiments that it outperforms existing belief propagation methods in terms of accuracy and computational efficiency. Supporting code is available at https://github.com/danmackinlay/GEnBP

Conrad Sanderson, Dan Pagendam, Brendan Power et al.

With the underlying aim of increasing efficiency of computational modelling pertinent for managing & protecting the Great Barrier Reef, we perform a preliminary investigation on the use of deep neural networks for opportunistic model emulation of APSIM models by repurposing an existing large dataset containing outputs of APSIM model runs. The dataset has not been specifically tailored for the model emulation task. We employ two neural network architectures for the emulation task: densely connected feed-forward neural network (FFNN), and gated recurrent unit feeding into FFNN (GRU-FFNN), a type of a recurrent neural network. Various configurations of the architectures are trialled. A minimum correlation statistic is used to identify clusters of APSIM scenarios that can be aggregated to form training sets for model emulation. We focus on emulating 4 important outputs of the APSIM model: runoff, soil_loss, DINrunoff, Nleached. The GRU-FFNN architecture with three hidden layers and 128 units per layer provides good emulation of runoff and DINrunoff. However, soil_loss and Nleached were emulated relatively poorly under a wide range of the considered architectures; the emulators failed to capture variability at higher values of these two outputs. While the opportunistic data available from past modelling activities provides a large and useful dataset for exploring APSIM emulation, it may not be sufficiently rich enough for successful deep learning of more complex model dynamics. Design of Computer Experiments may be required to generate more informative data to emulate all output variables of interest. We also suggest the use of synthetic meteorology settings to allow the model to be fed a wide range of inputs. These need not all be representative of normal conditions, but can provide a denser, more informative dataset from which complex relationships between input and outputs can be learned.

Stephanie Clark, Rob J Hyndman, Dan Pagendam et al.

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages to most currently available approaches. There is ample room for methodological developments in this area. The work is motivated by an application involving the prediction of water levels as a function of rainfall and other climate variables in an aquifer in eastern Australia.