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Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations

Alice Cicirello

TL;DR

This paper advocates Physics-Enhanced Machine Learning (PEML) as a principled framework to address dynamical-system challenges where data are scarce, uncertainties are pervasive, and decisions must be explainable. It presents a taxonomy of PEML strategies—Physics-Informed ML, Physics-Guided ML, and Physics-Encoded ML—along with four bias types that constrain learning and enable effective integration of physics with data. The authors discuss when to apply each PEML category, outline open challenges (metrics, validation, error detection, scalability), and highlight the potential of PEML to deliver robust, interpretable predictions and digital twins for engineering systems. The work aims to move beyond purely data-driven models toward reliable, physics-consistent inferences that support high-consequence engineering decision making.

Abstract

This position paper takes a broad look at Physics-Enhanced Machine Learning (PEML) -- also known as Scientific Machine Learning -- with particular focus to those PEML strategies developed to tackle dynamical systems' challenges. The need to go beyond Machine Learning (ML) strategies is driven by: (i) limited volume of informative data, (ii) avoiding accurate-but-wrong predictions; (iii) dealing with uncertainties; (iv) providing Explainable and Interpretable inferences. A general definition of PEML is provided by considering four physics and domain knowledge biases, and three broad groups of PEML approaches are discussed: physics-guided, physics-encoded and physics-informed. The advantages and challenges in developing PEML strategies for guiding high-consequence decision making in engineering applications involving complex dynamical systems, are presented.

Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations

TL;DR

This paper advocates Physics-Enhanced Machine Learning (PEML) as a principled framework to address dynamical-system challenges where data are scarce, uncertainties are pervasive, and decisions must be explainable. It presents a taxonomy of PEML strategies—Physics-Informed ML, Physics-Guided ML, and Physics-Encoded ML—along with four bias types that constrain learning and enable effective integration of physics with data. The authors discuss when to apply each PEML category, outline open challenges (metrics, validation, error detection, scalability), and highlight the potential of PEML to deliver robust, interpretable predictions and digital twins for engineering systems. The work aims to move beyond purely data-driven models toward reliable, physics-consistent inferences that support high-consequence engineering decision making.

Abstract

This position paper takes a broad look at Physics-Enhanced Machine Learning (PEML) -- also known as Scientific Machine Learning -- with particular focus to those PEML strategies developed to tackle dynamical systems' challenges. The need to go beyond Machine Learning (ML) strategies is driven by: (i) limited volume of informative data, (ii) avoiding accurate-but-wrong predictions; (iii) dealing with uncertainties; (iv) providing Explainable and Interpretable inferences. A general definition of PEML is provided by considering four physics and domain knowledge biases, and three broad groups of PEML approaches are discussed: physics-guided, physics-encoded and physics-informed. The advantages and challenges in developing PEML strategies for guiding high-consequence decision making in engineering applications involving complex dynamical systems, are presented.
Paper Structure (14 sections, 7 figures)

This paper contains 14 sections, 7 figures.

Table of Contents

  1. Introduction
  2. Why is there a need to go beyond data-driven for dynamical systems?
  3. Challenge one: the volume of useful data is generally limited
  4. Challenge two: avoiding accurate-but-wrong predictions
  5. Challenge three: dealing with uncertainty
  6. Challenge four: Explainable and Interpretable inferences
  7. Physics-Enhanced Machine Learning (PEML)
  8. Physics and domain knowledge biases to obtain a PEML architecture
  9. Three broad groups of PEML approaches
  10. Physics-Informed ML: $f({\bf x})\approx M[D({\bf x}_{measured}, {y}_{measured}, \boldsymbol{ \theta}_D)+biases)]$
  11. Physics-Guided ML: $f({\bf x})\approx M[G({\bf x}_{model}, \boldsymbol{ \theta}_p) + biases]$
  12. Physics-Encoded ML: $f({\bf x})\approx M[G({\bf x}_{model}, \boldsymbol{ \theta}_p) \cup D({\bf x}_{measured}, {y}_{measured}, \boldsymbol{ \theta}_D)+ biases]$
  13. Which PEML strategy should be used?
  14. Open challenges and opportunities with particular focus on dynamical systems

Figures (7)

  • Figure 1: Physics-based model analysis versus Machine Learning.
  • Figure 2: Errors introduced when building models of a dynamical system
  • Figure 3: Reducible and irreducible uncertainties
  • Figure 4: Influence of uncertainty on a performance metric versus availability of information to reduce or quantify uncertainty. Depending on the application medium and high influence of uncertainty columns might be swapped.
  • Figure 5: Summary of the four categories of biases.
  • ...and 2 more figures