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Mapping uncertainty using differentiable programming
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DOI：10.1002/aic.18940.png)
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Abstract
En 中文
Uncertainty quantification (UQ) and propagation is a ubiquitous challenge in science, permeating our field in a general fashion, and its importance cannot be overstated. Recently, the commoditization of differentiable programming, motivated by the development of machine learning, has allowed easier access to tools for evaluating derivatives of complex systems, of implicit and nonlinear nature. Motivated by this, we develop a UQ mapping approach based on differentiable programming principles. The approach is novel, faster, and yields equally accurate results when compared against the current state-of-the-art approaches for the UQ problem, which is to quantify and map uncertainty using linear methods or expensive Monte Carlo simulations. Three case studies—namely a continuous stirred tank reactor, a membrane reactor, and a fed-batch bioreactor—are assessed and compared against typical uncertainty mapping techniques. Lastly, the method allows the use of a single model implementation to perform forward and inverse uncertainty maps, easily switching mapping directions.
Keywords:
automatic differentiation
forward mapping
inverse mapping
inverse problems
uncertainty quantification
Journal
IF:
4
Papers:
1.1W
Citations:
2.9W