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In this article, we present a novel sampling method to improve the training accuracy of Physics-Informed Neural Networks (PINNs). Inspired by the idea of incremental learning in artificial intelligence, we propose a risk min–max framework to do the adaptive sampling. Within this framework, we develop a simple yet effective strategy known as Gaussian mixture distribution-based adaptive sampling (GAS), which enables us to achieve a lower error in the solution of PINNs with even fewer training epochs and samples. In practical training procedure, GAS uses the current residual information to generate a Gaussian mixture distribution for the sampling of additional points, which can be used to speed up the convergence of the loss and achieve higher accuracy. In our experiments with a two-peak Poisson problem, GAS achieves a mean square error of 1.5E−05, surpassing other sampling methods by two orders of magnitude. Other numerical examples on 2-dimensional and 10-dimensional problems further demonstrate that GAS consistently outperforms several existing adaptive methods in terms of accuracy and efficiency. In general, the proposed method can also be applied to various types of partial differential equations (PDEs), including the elliptic equations, wave equations and Burgers equations. [ABSTRACT FROM AUTHOR]

The first step in organ morphogenesis is the subdivision of a primordium into discrete regions by patterning genes. Recently, Burian et al. used live imaging and cell-lineage tracing to illuminate early patterning events during the establishment of leaf primordium adaxial–abaxial (dorsoventral) polarity, which clarifies controversies in the field. [ABSTRACT FROM AUTHOR]

The appearance of leaves with flattened laminae about 400 million years (Myr) ago had broad impacts on the Earth's ecosystem. The influential telome theory presents a model for this evolutionary transition, although it lacks plausible molecular evidence. Recently, microtubule-mediated mechanical feedback was proposed as a parsimonious alternative mechanism to explain leaf blade evolution. [ABSTRACT FROM AUTHOR]

Understanding how the genome encodes organismal shape is fundamental to biology. Extensive molecular genetic studies have uncovered genes regulating morphogenesis, that is, the generation of shape, however, such genes do not directly determine cell and tissue shape. Recent studies have started to elucidate how mechanical cues mediate the physical shaping of cells and tissues. In particular, the mechanical force generated during cell and tissue growth coordinates deformation at the tissue and organ scale. In this review, we summarize the recent progress of mechanical regulation of plant development. We focus our discussion on how patterns of mechanical stresses are formed, how mechanical cues are perceived, and how they guide cell and organ morphogenesis. [ABSTRACT FROM AUTHOR]

Plants differ from most animals in their retained ability to initiate new cycles of growth and development, which relies on the establishment and activity of branch meristems. In seed plants, branching is achieved by axillary meristems, which are established in the axil of each leaf base and develop into lateral branches. Research into axillary meristem initiation has identified transcription factors and phytohormones as key regulators. Based on these findings, a mechanistic framework for understanding axillary meristem initiation has emerged. Taking recent research into account, we discuss mechanisms underlying stem cell fate regulation that enable axillary meristem formation. [ABSTRACT FROM AUTHOR]

Summary: Unlike most animal cells, plant cells can easily regenerate new tissues from a wide variety of organs when properly cultured. The common elements that provide varied plant cells with their remarkable regeneration ability are still largely unknown. Here we describe the initial process of Arabidopsis in vitro regeneration, where a pluripotent cell mass termed callus is induced. We demonstrate that callus resembles the tip of a root meristem, even if it is derived from aerial organs such as petals, which clearly shows that callus formation is not a simple reprogramming process backward to an undifferentiated state as widely believed. Furthermore, callus formation in roots, cotyledons, and petals is blocked in mutant plants incapable of lateral root initiation. It thus appears that the ectopic activation of a lateral root development program is a common mechanism in callus formation from multiple organs. [Copyright &y& Elsevier]