Brown University

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

<i>The Physics of Liquid Crystals</i>

Part 1 Liquid crystals - main types and properties: introduction - what is a liquid crystal? the building blocks nematics and cholesterics smectics columnar phases more on long-, quasi-long and short-range order remarkable features of liquid crystals. Part 2 Long- and short-range order in nematics: definition of an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures. Part 3 Static distortion in a nematic single crystal: principles of the continuum theory magnetic field effects electric field effects in an insulating nematic fluctuations in the alignment hydrostatics of nematics. Part 4 Defects and textures in nematics: observations disclination lines point disclinations walls under magnetic fields umbilics surface disclinations. Part 5 Dynamical properties of nematics: the equations of nematodynamics experiments measuring the Leslie co-efficients convective instabilities under electric fields molecular motions. Part 6 Cholesterics: optical properties of an ideal helix agents influencing the pitch dynamical properties textures and defects in cholesterics. Part 7 Smectics: symmetry of the main smectic phases continuum description of smectics A and C remarks on phase and precritical phenomena.

<i>Scaling Concepts in Polymer Physics</i>

The Physics of Liquid Crystals

Abstract This new edition of this classic text on condensed matter physics includes the great advances that have taken place since its first publication in 1974. New chapters describe the main types and properties of liquid crystals in terms of the new phases discovered since the middle of the 1970's, and advances in the understanding of local order and the nature of the isotropic to nematic transition. There is an extensive discussion of the symmetry, and macroscopic and dynamic properties of smectics and columnar phases, and their defects, illustrated with numerous descriptions of experimental arrangements. The final chapter is devoted to phase transitions in smectics, including the celebrated analogy between Smectic A and superconductors. Throughout the book there is an emphasis on order-of-magnitude considerations. Its topicality and breadth of coverage will ensure that The Physics of Liquid Crystals remains an indispensable guide for students and researchers alike.

Physics-informed machine learning

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.

Opportunities and obstacles for deep learning in biology and medicine

Deep learning describes a class of machine learning algorithms that are capable of combining raw inputs into layers of intermediate features. These algorithms have recently shown impressive results across a variety of domains. Biology and medicine are data-rich disciplines, but the data are complex and often ill-understood. Hence, deep learning techniques may be particularly well suited to solve problems of these fields. We examine applications of deep learning to a variety of biomedical problems-patient classification, fundamental biological processes and treatment of patients-and discuss whether deep learning will be able to transform these tasks or if the biomedical sphere poses unique challenges. Following from an extensive literature review, we find that deep learning has yet to revolutionize biomedicine or definitively resolve any of the most pressing challenges in the field, but promising advances have been made on the prior state of the art. Even though improvements over previous baselines have been modest in general, the recent progress indicates that deep learning methods will provide valuable means for speeding up or aiding human investigation. Though progress has been made linking a specific neural network's prediction to input features, understanding how users should interpret these models to make testable hypotheses about the system under study remains an open challenge. Furthermore, the limited amount of labelled data for training presents problems in some domains, as do legal and privacy constraints on work with sensitive health records. Nonetheless, we foresee deep learning enabling changes at both bench and bedside with the potential to transform several areas of biology and medicine.

Protein Phase Separation: A New Phase in Cell Biology

Physics-informed neural networks (PINNs) for fluid mechanics: a review

Hyberbolic Conservation Laws in Continuum Physics