The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally ...intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods.
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Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well described by the Navier-Stokes ...equations, but solving these equations at scale remains daunting, limited by the computational cost of resolving the smallest spatiotemporal features. This leads to unfavorable trade-offs between accuracy and tractability. Here we use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows. For both direct numerical simulation of turbulence and large-eddy simulation, our results are as accurate as baseline solvers with 8 to 10× finer resolution in each spatial dimension, resulting in 40- to 80-fold computational speedups. Our method remains stable during long simulations and generalizes to forcing functions and Reynolds numbers outside of the flows where it is trained, in contrast to black-box machine-learning approaches. Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization.
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Fluids in natural systems, like the cytoplasm of a cell, often contain thousands of molecular species that are organized into multiple coexisting phases that enable diverse and specific functions. ...How interactions between numerous molecular species encode for various emergent phases is not well understood. Here, we leverage approaches from random-matrix theory and statistical physics to describe the emergent phase behavior of fluid mixtures with many species whose interactions are drawn randomly from an underlying distribution. Through numerical simulation and stability analyses, we show that these mixtures exhibit staged phase-separation kinetics and are characterized by multiple coexisting phases at steady state with distinct compositions. Random-matrix theory predicts the number of coexisting phases, validated by simulations with diverse component numbers and interaction parameters. Surprisingly, this model predicts an upper bound on the number of phases, derived from dynamical considerations, that is much lower than the limit from the Gibbs phase rule, which is obtained from equilibrium thermodynamic constraints. We design ensembles that encode either linear or nonmonotonic scaling relationships between the number of components and coexisting phases, which we validate through simulation and theory. Finally, inspired by parallels in biological systems, we show that including nonequilibrium turnover of components through chemical reactions can tunably modulate the number of coexisting phases at steady state without changing overall fluid composition. Together, our study provides a model framework that describes the emergent dynamical and steady-state phase behavior of liquid-like mixtures with many interacting constituents.
Fibroblasts are important cells for the support of homeostatic tissue function. In inflammatory diseases such as rheumatoid arthritis and inflammatory bowel disease, fibroblasts take on different ...roles (a) as inflammatory cells themselves and (b) in recruiting leukocytes, driving angiogenesis, and enabling chronic inflammation in tissues. Recent advances in single-cell profiling techniques have transformed the ability to examine fibroblast states and populations in inflamed tissues, providing evidence of previously underappreciated heterogeneity and disease-associated fibroblast populations. These studies challenge the preconceived notion that fibroblasts are homogeneous and provide new insights into the role of fibroblasts in inflammatory pathology. In addition, new molecular insights into the mechanisms of fibroblast activation reveal powerful cell-intrinsic amplification loops that synergize with primary fibroblast stimuli to result in striking responses. In this Review, we focus on recent developments in our understanding of fibroblast heterogeneity and fibroblast pathology across tissues and diseases in rheumatoid arthritis and inflammatory bowel diseases. We highlight new approaches to, and applications of, single-cell profiling techniques and what they teach us about fibroblast biology. Finally, we address how these insights could lead to the development of novel therapeutic approaches to targeting fibroblasts in disease.
Invariant natural killer T (iNKT) cells exist in a 'poised effector' state, which enables them to rapidly produce cytokines following activation. Using a nearly monospecific T cell receptor, they ...recognize self and foreign lipid antigens presented by CD1d in a conserved manner, but their activation can catalyse a spectrum of polarized immune responses. In this Review, we discuss recent advances in our understanding of the innate-like mechanisms underlying iNKT cell activation and describe how lipid antigens, the inflammatory milieu and interactions with other immune cell subsets regulate the functions of iNKT cells in health and disease.
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Individuals can function as integrated organisms only when information and resources are shared across a body. Signals and substrates are commonly moved using fluids, often channeled through a ...network of tubes. Peristalsis is one mechanism for fluid transport and is caused by a wave of cross-sectional contractions along a tube. We extend the concept of peristalsis from the canonical case of one tube to a random network. Transport is maximized within the network when the wavelength of the peristaltic wave is of the order of the size of the network. The slime mold Physarum polycephalum grows as a random network of tubes, and our experiments confirm peristalsis is used by the slime mold to drive internal cytoplasmic flows. Comparisons of theoretically generated contraction patterns with the patterns exhibited by individuals of P. polycephalum demonstrate that individuals maximize internal flows by adapting patterns of contraction to size, thus optimizing transport throughout an organism. This control of fluid flow may be the key to coordinating growth and behavior, including the dynamic changes in network architecture seen over time in an individual.
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Recent experiments have convincingly demonstrated the existence of surface nanobubbles on submerged hydrophobic surfaces. However, classical theory dictates that small gaseous bubbles quickly ...dissolve because their large Laplace pressure causes a diffusive outflux of gas. Here we suggest that the bubbles are stabilized by a continuous influx of gas near the contact line, due to the gas attraction towards hydrophobic walls Dammer and Lohse, Phys. Rev. Lett. 96, 206101 (2006); 10.1103/PhysRevLett.96.206101Zhang, Phys. Rev. Lett.10.1103/PhysRevLett.98.136101 98, 136101 (2007); 10.1103/PhysRevLett.98.136101Mezger, J. Chem. Phys. 128, 244705 (2008)10.1063/1.2931574. This influx balances the outflux and allows for a metastable equilibrium, which, however, vanishes in thermodynamic equilibrium. Our theory predicts the equilibrium radius of the surface nanobubbles, as well as the threshold for surface nanobubble formation as a function of hydrophobicity and gas concentration.
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The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between ...adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from δ-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.
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