Bayesian Physics Informed Neural Networks for Data Assimilation and Spatio-Temporal Modelling of Wildfires
Highlights
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A Bayesian physics-informed neural network that offers the capability for data assimulation while also providing uncertainty quantification. The method uses Bayes-by-backprop to provide quantitive epistemic uncertainty in predictions via the posterior distribution.
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Works over sparse and noisy data.
Summary
The level-set equation is typically applied to wildfire fire-front forecasting. The authors apply physics informed neural networks (PINN) to solve the level-set equation and simulate a fire-front as it moves through the spatio-temporal domain. Further, the authors augment their approach with Bayesian methods to produce a model that can quantify it's uncertainty and support operator decision making. They show their method is robust to extreme changes, such as sudden wind directions, that are typically detrimental to temporal continuity and lead to solutions that blatantly violate physical restraints.
Key Contributions
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A Bayesian physics-informed neural network that offers the capability for data assimulation while also providing uncertainty quantification. The method uses Bayes-by-backprop to provide quantitive epistemic uncertainty in predictions via the posterior distribution.
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The PINN is applied to solve the level-set equation and approximates constrained by the PDE residual.
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The PINN integrates observation and forecast likelihood, which work together to penalize deviations from PDE constraints as well as degenerate solutions (e.g. the PINN learning a flat or implausable surface that satisifies the PDE, yet is not realistic).
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Demonstrated on real overhead video data and simulated datasets.
Strengths
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Clear justification about why PINNs will work over a traditional PDE numerical solving method, especially with factors such as suddenly changing wind direction and speed.
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The uncertainty quantification via the use of Bayesian PINNs is fairly novel, giving a direct confidenence interval (e.g. 95%) to an operator.
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The data assimilation is useful when dealing with sparse and noisy realistic wildfire data. The data assimilation is done without breaking the PDE constraints.
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The math is clear, concise, and easy to follow.
Weaknesses / Questions
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The behavior the B-PINN is still fairly lackluster compared to the gold standard level set method both visually and in the evaluations. There is a clearly visible drawback to using this method.
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It's not clear how well this well work in complex realistic environments. The two real-world datasets listed are small-scale and only cover grasslands, not forests or mixed.
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35 pages of main body paper is quite a lot to read. The paper would have been much better served with sections of the methodology moved the appendix. Still, it was beneficial and comprehensive for learning the method.
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I'm not completely convinced on the bayesian prior calculation on real world data. I'd start with doing further sensitivity analysis on the prior variances.
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Calibrated uncertainty matters a lot in fire applications, and I feel it should have been better established in this paper.
Related Work
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Level Set Method
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Physics Informed Neural Networks
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Bayesian Physics Informed Neural Networks