With the rise in compute power over the past 10 years, we have seen a sharp increase in the number of simulations. Digital twins are one such example. They are virtual replicas of a physical object or process that can be simulated in a variety of scenarios.

One problem faced by digital twins is how they can combine potentially noisy empirical data with physics.
In 2021, researchers at the University of Sheffield developed a very simple digital twin framework called PhysiNet to solve this problem. PhysiNet combines Deep Learning with physics models to develop robust forecasts of device performance.
While digital twins do require significant development resources, they can be effective alternatives where physical tests are prohibitively expensive or dangerous.
Without further ado, let’s dive in…
Technical TLDR
Digital twins are electronic copies of physical systems. They rely on both black-box and rule-based (physics, economics, etc.) models. However, because both methods can fall short, we propose a combination of the two through a weighted linear combination of each models’ predicted values.
When iteratively training the black-box model, in each epoch we refit weights on both the models’ predictions to optimize accuracy. This linear combination of predictors effectively combines both models and optimizes accuracy.
But, what’s actually going on?
Let’s provide some background on digital twins and discuss the methods in the paper.
Background on Digital Twins
As stated above, digital twins are a digital copy of a physical thing, for instance a wind turbine or a supply chain. They’re often 3D models for physics-based products, but can be much simpler.
They were first used by NASA in 2010 to aid in the development of spacecrafts but gained popularity in applications where physical prototypes are difficult and/or expensive to test. Their most logical use case is during product ideation and development, but they can also be used along side a productionized product to gain insights and predict failures.
Industries that leverage digital twins range from product lifecycle management to building heating/cooling optimization to car sensors.
The Problem
Most digital twins rely heavily on either rules or empirical data. However, often the most robust models combine both a priori rules and empirical data. There are a variety of ways to do this, but PhysiNet proposes arguably the simplest solution.
The Solution
PhysiNet combines neural network (NN) forecasts with physics model forecasts. The neural network handles empirical data while the physics rules bound the system to reality – because real world data can be noisy, physics models are often quite helpful.
Let’s reference figure 1 below…

First, we fit our physics model (top), which is often a linear combination of variables. Because these models rarely take iterations to train, we are left with a static prediction.
Second, we fit a neural net (bottom). Neural networks leverage back-propagation over multiple epochs to train their weights. For each epoch, in addition to updating the weight vectors in the network, we also develop a forecast that combines the physics and NN forecast (shown in the green box).
Both of the weights, represented by w‘s, add up to 1. So, if the physics weight is equal to 0, we only use the NN prediction and visa versa. Depending upon the quality of physics and empirical data, this framework automatically updates our predicted values to optimize accuracy.

As shown in figure 2 above, this incredibly simple framework boasts performance improvements relative to either model alone. Physics models tend to oversimplify and neural nets require lots of high-quality data, so by combining both models we can avoid both shortcomings.
Summary
Digital twins are efficient alternatives to expensive physical tests. For physics-based simulations, PhysiNet combines weighted predictions of both a physics model and a black-box Machine Learning model. This framework boasts accuracy improvements relative to either model alone.
The framework is incredibly simple and can be extended, for instance by using physics model forecasts as features in the neural net. If you have resources/opinions on the topic, please leave a comment. It would be much appreciated!
Thanks for reading! I’ll be writing 33 more posts that bring academic research to the DS industry. Check out my comment for links to the main source for this post and some useful resources.