A framework based on symbolic regression coupled with eXtended Physics-Informed Neural Networks for gray-box learning of equations of motion from data

Elham, Kiyani,; Shukla, K. K.; Karniadakis, George Em; Karttunen, Mikko

doi:10.1016/j.cma.2023.116258

Cited by 10 publications

(5 citation statements)

References 48 publications

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“…The method employed to find unknown parameters in this study exhibits potential for broader applications, such as different fluid properties, reduced-order PDEs, and scenarios in which only a part of the equation is absent (grey box learning framework; Kiyani et al 2023). While, potentially, the parameters of the proposed ODE could be discovered using other aforementioned approaches for the purpose of this paper, the scalability and extensibility to PDEs or more complex ODEs, and insensitivity to initial conditions in the fitting process compared to other methods, suggest that PINNs are the most suitable choice for this task.…”

Section: Physics-informed Neural Networkmentioning

confidence: 99%

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

Kiyani,

Kooshkbaghi,

Shukla

et al. 2024

J. Fluid Mech.

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The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

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Section: Physics-informed Neural Networkmentioning

confidence: 99%

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

Kiyani,

Kooshkbaghi,

Shukla

et al. 2024

J. Fluid Mech.

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“…Students can learn how GAs mimic the process of natural selection and evolution to find optimal solutions to problems. For instance, they can explore how GA can be used to optimise parameters in physics experiments or engineering designs [16]. By actively participating in the creation and modification of GAs, students gain hands-on experience in programming and algorithm design, thereby enhancing their computational and mathematical skills [17].…”

Section: Use Of Gas In Stemmentioning

confidence: 99%

Fostering scientific methods in simulations through symbolic regressions

Llorella,

Antonio Cebrián,

Corbi

et al. 2024

Phys. Educ.

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Two-dimensional computer and tablet PC physics simulations have proved to be effective in helping students understand the fundamental principles of physics and related natural processes. However, the current approach to using these simulations tends to follow a repetitive cognitive and procedural pathway, regardless of the specific physical concepts being explored or software environment being used. This approach involves manipulating the simulation interface and collecting data through interaction with controls, widgets, or other contextual elements. Students then attempt to determine how these experimental measurements align with established laws, interactions, or mechanisms, as the teacher might have previously explained. We believe that this approach, while appropriate for education, obscures scientific processes, mainly related to the hypothetico-deductive model. To address this issue, we have developed a simple and adaptable computer environment that makes use of genetic algorithms (GAs) and symbolic regression to derive many of the basic laws of nature from the data collected by students using the popular physics education technology (PhET) simulations environment. Our proposal enables learners to observe how the order and relationships of mathematical tokens are routinely refined as new data points are added to the simulation setting. This iterative distillation technique can also be augmented with the interplay of dimensional analysis. In contrast with other more sophisticated artificial intelligence patterns, GA fit into the realm of grey box machine learning models. These type of evolutionary algorithms achieve the sought results by evolving mathematical models on each stage in an understandable way, which mimics the way scientific breakthroughs are accomplished (over the course of generations of researchers and based of prior knowledge). By implementing this innovative approach, we can provide students with a more authentic empirical experience that fosters a deeper understanding of the principles of science and scientific discovery. Field tests with students supporting this claim have also been carried out.

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“…Moreover, when confronted with equations containing unknown components expressed as functions, the PINN [149,150] method may be more suitable. Kiyani et al [158] employed an improved PINN approach to successfully discover the functional form used to describe the nonlinear term in the phase-field model. Subsequently, utilizing symbolic regression techniques, they deduced the explicit mathematical formula for this unknown component.…”

Section: Extracting Continuum Equationsmentioning

confidence: 99%

“…In addition, symbolic regression is a white-box model that can be especially effective for problems where an analytic solution exists but is unknown, like extracting the unknown components of equations. [158] Nevertheless, this assumption may not be valid in most cases. Tree-based models are another effective and widely used white-box models, [68,252,300] which can internally reason about its entire decision-making process.…”

Section: Conclusion and Prospectsmentioning

confidence: 99%

Machine Learning in Soft Matter: From Simulations to Experiments

Zhang,

Gong,

Jiang

2024

Adv Funct Materials

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Soft matter with diverse functionalities that are easily designable has fascinated tremendous research interests in the past several decades. Nevertheless, the inherent confluence of time and length scale ubiquitous in soft matter immensely complicates the elucidation of the structure–property relationship and thereby severely impedes the function exploration of soft materials. Recently, the emergent machine learning (ML) techniques open new paradigms in property prediction and molecular design of functional materials, due to their extraordinarily distinguished performance in the aspect of trend identity and pattern extraction from data, and objective optimization by accelerating the guided search in high‐dimensional spaces. This review exclusively focuses on the current state‐of‐the‐art progress in the development of ML techniques applied in the realms of soft matter, ranging from coarse‐grained simulations to theoretical prediction on the structural formation and macroscopic properties, as well as the optimization and algorithm‐aided design in experiments. Finally, an outlook on the challenges and opportunities for this rapidly evolving field is discussed.

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A framework based on symbolic regression coupled with eXtended Physics-Informed Neural Networks for gray-box learning of equations of motion from data

Cited by 10 publications

References 48 publications

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

Fostering scientific methods in simulations through symbolic regressions

Machine Learning in Soft Matter: From Simulations to Experiments

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