Physics-Guided Deep Learning for Dynamical Systems: A survey

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are interpretable but rely on rigid assumptions. And the direct numerical approximation is usually computationally intensive, requiring significant computational resources and expertise. While deep learning (DL) provides novel alternatives for efficiently recognizing complex patterns and emulating nonlinear dynamics, it does not necessarily obey the governing laws of physical systems, nor do they generalize well across different systems. Thus, the study of physics-guided DL emerged and has gained great progress. It aims to take the best from both physics-based modeling and state-of-the-art DL models to better solve scientific problems. In this paper, we provide a structured overview of existing methodologies of integrating prior physical knowledge or physics-based modeling into DL and discuss the emerging opportunities

Polyconvex anisotropic hyperelasticity with neural networks

In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. In addition, the models are calibrated with transversely isotropic data, generated with an analytical polyconvex potential. For this case, both models show excellent results, demonstrating the straightforward applicability of the polyconvex neural network constitutive models to other symmetry groups

A Machine Learning based approach to predict road rutting considering uncertainty

Roads as vital public assets are the backbone for transportation systems and support constant societal development. Recently, data-driven technologies such as digital twins and especially machine learning have shown great potential to maintain the service level of the existing road infrastructure by accurate future condition modelling and optimal maintenance treatment recommendations. However, the pavement community suffers from inadequate data and errors experienced in data collection, which unavoidably limits machine learning performance. In addition, focusing solely on data without considering the underlying physical behaviour remains as a challenge for the practical implementation of machine learning. To this end, this study provides a machine learning based approach to predict road rutting taking into account the machine learning uncertainties. The US Long-Term Pavement Performance public database has been used as the main data source while supplementary synthetic data was added using Finite Element simulations based on physics. The obtained results indicate that adding extra simulation data improved the model’s short-term prediction accuracy by 4.4% and reduced the long-term prediction uncertainty by 6.76%. The approach could potentially mitigate the issue of lack of data and the uncertainties around the data collected, by integrating existing understanding of pavement physical behaviour into the machine learning modelling pipeline

Random scattering of surface plasmons for sensing and tracking

In this thesis, a single particle biosensing setup, capable of sensing and tracking single nanoscale biological particles, is proposed and investigated theoretically. The setup is based on monitoring the speckle pattern intensity distribution arising due to random scattering of surface plasmon polaritons (SPPs) from a metal surface. An analyte particle close to the surface will additionally scatter light, perturbing the speckle pattern. From this speckle pattern perturbation, the analyte particle can be detected and tracked. Theoretical sensitivity analysis predicts a biological particle on the order of 10nm in radius gives a fractional intensity perturbation to the speckle intensity of 10^4, comparable to intensity contrasts used in existing interferometric scattering sensing techniques. A formula for the minimum detectable particle size is derived. In addition, an algorithm is derived capable of extracting the particle trajectory in the single scattering regime from the change to the speckle intensity perturbation over time and shown to be capable of errors of approximately 1nm on simulated data under optimal noise conditions. The effect of multiple scattering on the speckle pattern perturbation is studied, and it is shown that, by tuning the scattering mean free path and individual scatterer properties of a random nanostructure of scatterers on the metal surface, one can increase the magnitude of the speckle field perturbation by up to the order of 10^2. A neural network based localisation algorithm is developed to calculate the analyte particle position based on the speckle intensity perturbation and its performance on simulated data is studied. Mean errors on the order of 20nm were found, depending on the size of the region over which the particle must be tracked. Unlike the single scattering tracking algorithm, the neural network algorithm continues to function in the multiple scattering regime.Open Acces

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science