Periodic Reporting for period 3 - PhyCo (Physics-constrained adaptive learning for multi-physics optimization)
Reporting period: 2023-05-01 to 2024-10-31
Trillions of bytes of data have been created in the world while reading this very sentence.
The traditional triad of the scientific method, theory, experimentation and simulation has added big data now.
Central to big data science are artificial intelligence and machine learning, which are automated ways of transforming information into empirical knowledge.
Whereas empirical knowledge is crucial to many practical applications, such as facial recognition, empirical models do not necessarily fulfil physical principles, for example, conservation laws.
Physical principles provide physical equations, which are essential to understanding, modelling and, ultimately, designing engineering systems that optimize a performance.
One of the most prominent engineering and scientific communities that has been working with big data and physical principles for decades is fluid mechanics.
Fluid mechanics underpins many established and emerging world-wide industries as well as critical societal issues such as climate science and energy consumption.
These problems involve flows that are unsteady, unpredictable and uncertain across a vast range of spatiotemporal scales.
Because of this, numerical simulations and experimental measurements of the physics of fluids generate big data, which is to say that fluid mechanics is both a physical and big data discipline.
To gain insight into this big data, machine learning techniques have recently been applied to benchmark fluids problems with success, but there are still three big open questions:
(i) Do machine learning algorithms scale to engineering configurations? (Are they robust?);
(ii) Can we gain physical insight into the solutions? (Are they interpretable?); and
(iii) Can we extrapolate knowledge to other configurations, such as multi-physics phenomena? (Are they generalizable?).
Key to this project is the simple, but important, observation that the ability of fluid mechanics modelling to predict the evolution of a flow is enabled by both empirical approaches and physical principles.
Machine learning models may not be interpretable, robust and generalizable, but they enable adaptive empirical modelling.
On the other hand, physical principles are governed by “rigid equations”, i.e. they do not adaptively change, but they are interpretable, robust and generalizable.
Machine learning is excellent at finding correlations in big data, whereas human beings are excellent at extrapolating knowledge (physical principles).
This project will integrate the complementary capabilities of both approaches to achieve adaptive modelling for optimization of unsteady, unpredictable and uncertain multi-physics flows.
These are flows of paramount importance in engineering, which are intractable to modelling and optimization.
This project will combine physical principles and empirical modelling into a unified approach: physics-constrained adaptive learning.
The technical objectives are
(i) to combine physical principles with machine learning empirical modelling into a unified approach;
(ii) to design adaptive multi-physics models by on-the-fly assimilation of experimental measurements (direct problem);
(iii) to optimize unsteady, unpredictable and uncertain flows (inverse problem);
(iv) to accompany the predictions with robust uncertainty quantification;
and (v) to develop a code that wraps around existing high-fidelity simulation software and experimental rigs.
The computational technology will be applied to maximize energy harvesting from aeroelastic systems to produce clean energy;
optimize clean and stable aeroengines with lean flames for low emissions; and reconstruct high-resolution physics from low-resolution experimental measurements to maximize physical information to assimilate in our simulations.
The vision is that machine learning methods will go hand in hand with the art of constructing physical models.
This has the potential to revolutionize the engineering design of multi-physics fluid dynamics systems, and beyond.
The traditional triad of the scientific method, theory, experimentation and simulation has added big data now.
Central to big data science are artificial intelligence and machine learning, which are automated ways of transforming information into empirical knowledge.
Whereas empirical knowledge is crucial to many practical applications, such as facial recognition, empirical models do not necessarily fulfil physical principles, for example, conservation laws.
Physical principles provide physical equations, which are essential to understanding, modelling and, ultimately, designing engineering systems that optimize a performance.
One of the most prominent engineering and scientific communities that has been working with big data and physical principles for decades is fluid mechanics.
Fluid mechanics underpins many established and emerging world-wide industries as well as critical societal issues such as climate science and energy consumption.
These problems involve flows that are unsteady, unpredictable and uncertain across a vast range of spatiotemporal scales.
Because of this, numerical simulations and experimental measurements of the physics of fluids generate big data, which is to say that fluid mechanics is both a physical and big data discipline.
To gain insight into this big data, machine learning techniques have recently been applied to benchmark fluids problems with success, but there are still three big open questions:
(i) Do machine learning algorithms scale to engineering configurations? (Are they robust?);
(ii) Can we gain physical insight into the solutions? (Are they interpretable?); and
(iii) Can we extrapolate knowledge to other configurations, such as multi-physics phenomena? (Are they generalizable?).
Key to this project is the simple, but important, observation that the ability of fluid mechanics modelling to predict the evolution of a flow is enabled by both empirical approaches and physical principles.
Machine learning models may not be interpretable, robust and generalizable, but they enable adaptive empirical modelling.
On the other hand, physical principles are governed by “rigid equations”, i.e. they do not adaptively change, but they are interpretable, robust and generalizable.
Machine learning is excellent at finding correlations in big data, whereas human beings are excellent at extrapolating knowledge (physical principles).
This project will integrate the complementary capabilities of both approaches to achieve adaptive modelling for optimization of unsteady, unpredictable and uncertain multi-physics flows.
These are flows of paramount importance in engineering, which are intractable to modelling and optimization.
This project will combine physical principles and empirical modelling into a unified approach: physics-constrained adaptive learning.
The technical objectives are
(i) to combine physical principles with machine learning empirical modelling into a unified approach;
(ii) to design adaptive multi-physics models by on-the-fly assimilation of experimental measurements (direct problem);
(iii) to optimize unsteady, unpredictable and uncertain flows (inverse problem);
(iv) to accompany the predictions with robust uncertainty quantification;
and (v) to develop a code that wraps around existing high-fidelity simulation software and experimental rigs.
The computational technology will be applied to maximize energy harvesting from aeroelastic systems to produce clean energy;
optimize clean and stable aeroengines with lean flames for low emissions; and reconstruct high-resolution physics from low-resolution experimental measurements to maximize physical information to assimilate in our simulations.
The vision is that machine learning methods will go hand in hand with the art of constructing physical models.
This has the potential to revolutionize the engineering design of multi-physics fluid dynamics systems, and beyond.
Multi-disiplinarity is at the core of PhyCo. PhyCo is proposing digital twins by developing models that work in real-time and learns to become more accurate.
PhyCo is at the forefront of scientific machine learning, also known as AI for Science.
First, PhyCo is combining physical principles with machine learning empirical modelling into a unified approach.
Machine learning tools do not fulfil the governing equations and physical constraints a priori.
We have designed machine learning algorithms to be more interpretable, robust and generalizable.
We are reducing data requirements to accelerate the training on the fly.
Second, PhyCo is designing adaptive multi-physics models by on-the-fly assimilation of experimental measurements.
We have discovered the multi-physics equations of acoustics-reacting flow interaction for indirect sound generation.
We have combined the prior knowledge on the acoustics and reaction rates in form of qualitative and cheap low-order models to assimilate data from sensors on the fly.
Third, PhyCo is optimizing unsteady, unpredictable and uncertain flows.
There exist very few methods to optimize chaotic and turbulent flows with affordable computations.
All of them have limitations.
We have designed sensitivity methods to calculate the gradient of the time average of an objective functional without the implementation of an adjoint code.
Fourth, PhyCo is quantifying rigorously how much we should trust engineering models.
Experimental measurements are typically accompanied by their uncertainties (“error bars”), but predictions from numerical simulations are customarily not.
With a Bayesian formalism, we change the question from determining one single solution to finding a set of solutions that are probabilistically likely to represent the multi-physics.
This has been applied to wind farm optimisation, spray optimization, and thermoacoustic modelling of hydrogen-based gas turbines.
Fifth, Phyco id develop a code that wraps around existing high-fidelity simulation software and experimental rigs.
The European Union, national funding bodies and companies have invested in code development for high-fidelity simulations, which resulted in excellent codes after years of development.
We have designed open-source that wrap around these existing high-fidelity codes non-intrusively (notably XCompact3D for high-fidelity simulations in turbulence, and Basilisk for multi-phase flows).
PhyCo is at the forefront of scientific machine learning, also known as AI for Science.
First, PhyCo is combining physical principles with machine learning empirical modelling into a unified approach.
Machine learning tools do not fulfil the governing equations and physical constraints a priori.
We have designed machine learning algorithms to be more interpretable, robust and generalizable.
We are reducing data requirements to accelerate the training on the fly.
Second, PhyCo is designing adaptive multi-physics models by on-the-fly assimilation of experimental measurements.
We have discovered the multi-physics equations of acoustics-reacting flow interaction for indirect sound generation.
We have combined the prior knowledge on the acoustics and reaction rates in form of qualitative and cheap low-order models to assimilate data from sensors on the fly.
Third, PhyCo is optimizing unsteady, unpredictable and uncertain flows.
There exist very few methods to optimize chaotic and turbulent flows with affordable computations.
All of them have limitations.
We have designed sensitivity methods to calculate the gradient of the time average of an objective functional without the implementation of an adjoint code.
Fourth, PhyCo is quantifying rigorously how much we should trust engineering models.
Experimental measurements are typically accompanied by their uncertainties (“error bars”), but predictions from numerical simulations are customarily not.
With a Bayesian formalism, we change the question from determining one single solution to finding a set of solutions that are probabilistically likely to represent the multi-physics.
This has been applied to wind farm optimisation, spray optimization, and thermoacoustic modelling of hydrogen-based gas turbines.
Fifth, Phyco id develop a code that wraps around existing high-fidelity simulation software and experimental rigs.
The European Union, national funding bodies and companies have invested in code development for high-fidelity simulations, which resulted in excellent codes after years of development.
We have designed open-source that wrap around these existing high-fidelity codes non-intrusively (notably XCompact3D for high-fidelity simulations in turbulence, and Basilisk for multi-phase flows).
The research achievements and methodologies originating from PhyCo are driving innovation across diverse fields, demonstrating a capacity for cross-disciplinary impact. Techniques developed through the grant, such as real-time data assimilation and physics-aware adaptive learning, are being adapted and extended to address challenges associated with achieving a net-zero society.
Real-time data assimilation methods are being applied to reduce the electricity consumption of electric road vehicles. This involves the design of real-time digital optimization and decision-making frameworks tailored for energy and transport systems. Similarly, gradient-free optimization techniques are being utilized to enhance wind turbine efficiency. By combining high-fidelity simulations with surrogate modeling, these methods aim to maximize power extraction. Furthermore, PhyCo's influence extends to quantum computing, where it is pioneering quantum algorithms for learning chaotic systems.
Real-time data assimilation methods are being applied to reduce the electricity consumption of electric road vehicles. This involves the design of real-time digital optimization and decision-making frameworks tailored for energy and transport systems. Similarly, gradient-free optimization techniques are being utilized to enhance wind turbine efficiency. By combining high-fidelity simulations with surrogate modeling, these methods aim to maximize power extraction. Furthermore, PhyCo's influence extends to quantum computing, where it is pioneering quantum algorithms for learning chaotic systems.