KE Hub Triage Workshop: SLB

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KE Hub Triage Workshop: SLB

 14 Jun 2024
1000 BST


KE Hub online Triage Workshops are organised with support from the ICMS


The next KE Hub online Triage Workshop will be presented by SLB.

Physics informed surrogate models for nonlinear partial differential equations with variable coefficients

Partial Differential Equations (PDEs) are ubiquitous in modelling physical phenomena across various scientific disciplines and solving them accurately can be computationally expensive and challenging, especially for complex systems. Physics Informed Machine Learning (PIML) bridges this gap by incorporating the underlying physical laws and constraints into machine learning algorithms. This approach not only accelerates the modelling process but also enhances the robustness and interpretability of machine learning models, making it a transformative tool for tackling complex problems in science and engineering. There are certain limitations around using this technology. The network is used to compute the partial derivatives for the PDE using automatic differentiation in order to setup the loss function. This has shown to work for a set of PDEs but not much work has been published on PDEs containing discrete variable coefficients that are nonlinear in the state variable. In addition, it is complicated to resolve all the constitutive physics and chemistry that is used in the numerical simulators.


In this workshop, we will look at a problem around modelling fluid flow in heterogeneous porous media. A method is introduced in which a commercial fluid flow simulator can be used to compute the loss function while training a PIML model. The aim is to compute the loss function accurately using the physical implementation available within the numerical simulator without explicitly coding any physical constraints in the network. The challenge is to converge the gradient descent iterations while training the network only using the gradients coming from the numerical simulator for an ensemble of model descriptions.

Academic mathematical scientists from KE Hub partner university departments are invited to take part in these workshops. If you would like to attend, please contact your local KE Champion to receive the meeting link or get in touch with the organisers, Lauren Hyndman and Diwei Zhou.



KE Hub Triage Workshops are informal discussion sessions where one B.I.G. Partner presents a challenge they are currently facing, with the aim of determining:

  1. What, if any, mathematical sciences approaches can be used to address the challenge?
  2. Who from the mathematical sciences community would like to take on the challenge?
  3. What mechanisms are most appropriate for driving the challenge forward?

The purpose of these workshops is to allow the B.I.G. Partner to engage directly with academic mathematical scientists to probe the scientific content of their proposed challenge. The environment is relaxed and interactive, and we encourage questions, clarifications and discussions throughout. You can find information on all upcoming and past workshops here.