The Kitchin Research Group

In our latest work, we set out to tackle a common challenge in engineering and science: understanding how small uncertainties in inputs, like temperature changes or slight variations in pressure, can ripple through complex systems and affect the final outcome. Instead of relying on slow, trial-and-error simulations, we leveraged an emerging computing technique that treats uncertainty like a path we can follow mathematically. By "teaching" our software to calculate these paths directly, we can predict how errors build up in real processes, whether in a chemical reactor, a filtration system, or a bioreactor, 100 times faster than traditional methods. This speed and precision mean we can design safer, more reliable systems and respond more quickly when things don't go exactly as planned.

We introduce a differentiable-programming-based framework for uncertainty quantification that leverages the implicit function theorem and path integration to compute both forward and inverse uncertainty maps directly from high-fidelity or surrogate models . Our approach requires only C¹ differentiability and injectivity of the implicit system and avoids expensive Monte Carlo sampling by tracing uncertainty "contours" through the model. We validate it on three chemical-engineering case studies: a CSTR (showing exact agreement with analytical solutions in unimodal and multimodal scenarios), a membrane reactor for natural-gas aromatization (recovering 95% of exhaustive-search samples in 7 min vs. ~10 h), and a fed-batch bioreactor with 3D ellipsoidal uncertainty regions. All code and reproducible Jupyter notebooks are available at github.com/KitchinHUB/Mapping-Uncertainty-Using-Differentiable-Programming.

@article{alves-2025-mappin-uncer,
  author =       {Victor Alves and Carl D. Laird and Fernando V. Lima and John
                  R. Kitchin},
  title =        {Mapping Uncertainty Using Differentiable Programming},
  journal =      {AIChE Journal},
  volume =       {},
  number =       {},
  pages =        {e18940},
  year =         2025,
  doi =          {10.1002/aic.18940},
  url =          {https://doi.org/10.1002/aic.18940},
  DATE_ADDED =   {Thu Jul 31 09:53:53 2025},
}

Copyright (C) 2025 by John Kitchin. See the License for information about copying.

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