Hybrid Surface Mesh Adaptation for Climate Modeling

Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest.A sec- ond,less-popular method of spatial adaptivity is called'mesh motion'(r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales.This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function,the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone.Further,in an attempt to support the requirements of a very general class of climate simulation applications,the proposed method is de- signed to accommodate unstructured,polygonal mesh topologies in addition to the most popular mesh types.

A Data Analysis Framework for Earth System Simulation within an <i>In-Situ</i>Infrastructure

This paper presents a generic procedure to implement a scalable and high performance data analysis framework for large-scale scientific simulation within an in-situ infrastructure. It demonstrates a unique capability for global Earth system simulations using advanced computing technologies (i.e., automated code analysis and instrumentation), in-situ infrastructure (i.e., ADIOS) and big data analysis engines (i.e., SciKit-learn). This paper also includes a useful case that analyzes a globe Earth System simulations with the integration of scalable in-situ infrastructure and advanced data processing package. The in-situ data analysis framework can provides new insights on scientific discoveries in multiscale modeling paradigms.

The physics and astrophysics of Type Ia supernova explosions

Asupernowt is a transient astronomical event of spectacular peak brightness that is associ-a ted with an exploding star. Supernovae exhibit a range of observational characteristics that historically h^ts led to a rich set of classsifications and sub-clmssifications. Despite the complex- ity of the obscrwttionally-based supernova, taxonomy, we now believe that all supernovae are caused by just one of two basic inechanisms： （i） the collapse of the core of a inassive star late in its litb, or （ii） a runaway thermonuclear explosion in a white dwarf. The former is terlned tile cor^-collapsc mechanism, and is powered by gravitational energy

Benchmarking graph neural networks for materials chemistry

Graph neural networks(GNNs)have received intense interest as a rapidly expanding class of machine learning models remarkably well-suited for materials applications.To date,a number of successful GNNs have been proposed and demonstrated for systems ranging from crystal stability to electronic property prediction and to surface chemistry and heterogeneous catalysis.However,a consistent benchmark of these models remains lacking,hindering the development and consistent evaluation of new models in the materials field.Here,we present a workflow and testing platform,MatDeepLearn,for quickly and reproducibly assessing and comparing GNNs and other machine learning models.We use this platform to optimize and evaluate a selection of top performing GNNs on several representative datasets in computational materials chemistry.From our investigations we note the importance of hyperparameter selection and find roughly similar performances for the top models once optimized.We identify several strengths in GNNs over conventional models in cases with compositionally diverse datasets and in its overall flexibility with respect to inputs,due to learned rather than defined representations.Meanwhile several weaknesses of GNNs are also observed including high data requirements,and suggestions for further improvement for applications in materials chemistry are discussed.

A SPARSE-GRID METHOD FOR MULTI-DIMENSIONAL BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

A sparse-grid method for solving multi-dimensional backward stochastic differential equations （BSDEs） based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathe- matical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and （adaptive） hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our scheme.

A bridge for accelerating materials by design

Recent technical advances in the area of nanoscale imaging,spectroscopy and scattering/diffraction have led to unprecedented capabilities for investigating materials structural,dynamical and functional characteristics.In addition,recent advances in computational algorithms and computer capacities that are orders of magnitude larger/faster have enabled large-scale simulations of materials properties starting with nothing but the identity of the atomic species and the basic principles of quantum and statistical mechanics and thermodynamics.Along with these advances,an explosion of high-resolution data has emerged.This confluence of capabilities and rise of big data offer grand opportunities for advancing materials sciences but also introduce several challenges.In this perspective,we identify challenges impeding progress towards advancing materials by design(e.g.,the design/discovery of materials with improved properties/performance),possible solutions and provide examples of scientific issues that can be addressed using a tightly integrated approach where theory and experiments are linked through big-deep data.

A FIRST-ORDER NUMERICAL SCHEME FOR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN BOUNDED DOMAINS

We propose a novel numerical scheme for decoupled forward-backward stochastic differ- ential equations （FBSDEs） in bounded domains, which corresponds to a class of nonlinear parabolic partial differential equations with Dirichlet boundary conditions. The key idea is to exploit the regularity of the solution （Yt,Zt） with respect to Xt to avoid direct ap- proximation of the involved random exit time. Especially, in the one-dimensional case, we prove that the probability of Xt exiting the domain within At is on the order of O（（△t）ε exp（--1/（△t）2ε））, if the distance between the start point X0 and the boundary is 1 g at least on the order of O（△t）^1/2-ε ） for any fixed c 〉 0. Hence, in spatial discretization, we set the mesh size △x - （9（（At）^1/2-ε ）, so that all the interior grid points are sufficiently far from the boundary, which makes the error caused by the exit time decay sub-exponentially with respect to △t. The accuracy of the approximate solution near the boundary can be guaranteed by means of high-order piecewise polynomial interpolation. Our method is developed using the implicit Euler scheme and cubic polynomial interpolation, which leads to an overall first-order convergence rate with respect to △t.

Use of the Spatial kD-Tree in Computational Physics Applications

The need to perform spatial queries and searches is commonly encountered within the field of computational physics.The development of applications ranging from scientific visualization to finite element analysis requires efficient methods of locating domain objects relative to general locations in space.Much of the time,it is possible to form and maintain spatial relationships between objects either explicitly or by using relative motion constraints as the application evolves in time.Occasionally,either due to unpredictable relative motion or the lack of state information,an application must perform a general search(or ordering)of geometric objects without any explicit spatial relationship information as a basis.If previous state information involving domain geometric objects is not available,it is typically an involved and time consuming process to create object adjacency information or to order the objects in space.Further,as the number of objects and the spatial dimension of the problem domain is increased,the time required to search increases greatly.This paper proposes an implementation of a spatial k-d tree(skD-tree)for use by various applications when a general domain search is required.The skD-tree proposed in this paper is a spatial access method where successive tree levels are split along different dimensions.Objects are indexed by their centroid,and the minimum bounding box of objects in a node are stored in the tree node.The paper focuses on a discussion of efficient and practical algorithms for multidimensional spatial data structures for fast spatial query processing.These functions include the construction of a skD-tree of geometric objects,intersection query,containment query,and nearest neighbor query operations.

Inverse design of two-dimensional materials with invertible neural networks

The ability to readily design novel materials with chosen functional properties on-demand represents a next frontier in materials discovery.However,thoroughly and efficiently sampling the entire design space in a computationally tractable manner remains a highly challenging task.To tackle this problem,we propose an inverse design framework(MatDesINNe)utilizing invertible neural networks which can map both forward and reverse processes between the design space and target property.This approach can be used to generate materials candidates for a designated property,thereby satisfying the highly sought-after goal of inverse design.We then apply this framework to the task of band gap engineering in two-dimensional materials,starting with MoS_(2).Within the design space encompassing six degrees of freedom in applied tensile,compressive and shear strain plus an external electric field,we show the framework can generate novel,high fidelity,and diverse candidates with near-chemical accuracy.We extend this generative capability further to provide insights regarding metal-insulator transition in MoS_(2)which are important for memristive neuromorphic applications,among others.This approach is general and can be directly extended to other materials and their corresponding design spaces and target properties.

Deep data analytics for genetic engineering of diatoms linking genotype to phenotype via machine learning

Genome engineering for materials synthesis is a promising avenue for manufacturing materials with unique properties under ambient conditions.Biomineralization in diatoms,unicellular algae that use silica to construct micron-scale cell walls with nanoscale features,is an attractive candidate for functional synthesis of materials for applications including photonics,sensing,filtration,and drug delivery.Therefore,controllably modifying diatom structure through targeted genetic modifications for these applications is a very promising field.In this work,we used gene knockdown in Thalassiosira pseudonana diatoms to create modified strains with changes to structural morphology and linked genotype to phenotype using supervised machine learning.An artificial neural network(NN)was developed to distinguish wild and modified diatoms based on the SEM images of frustules exhibiting phenotypic changes caused by a specific protein(Thaps3_21880),resulting in 94% detection accuracy.Class activation maps visualized physical changes that allowed the NNs to separate diatom strains,subsequently establishing a specific gene that controls pores.A further NN was created to batch process image data,automatically recognize pores,and extract pore-related parameters.Class interrelationship of the extracted paraments was visualized using a multivariate data visualization tool,called CrossVis,and allowed to directly link changes in morphological diatom phenotype of pore size and distribution with changes in the genotype.

Tensor factorization for elucidating mechanisms of piezoresponse relaxation via dynamic Piezoresponse Force Spectroscopy

Spatially resolved time and voltage-dependent polarization dynamics in PbTiO3 thin films is explored using dynamic piezoresponse force microscopy(D-PFM)in conjunction with interferometric displacement sensing.This approach gives rise to 4D data sets containing information on bias-dependent relaxation dynamics at each spatial location without long-range electrostatic artifacts.To interpret these data sets in the absence of defined physical models,we employ a non-negative tensor factorization method which clearly presents the data as a product of simple behaviors allowing for direct physics interpretation.Correspondingly,we perform phase-field modeling finding the existence of‘hard’and‘soft’domain wall edges.This approach can be extended to other multidimensional spectroscopies for which even exploratory data analysis leads to unsatisfactory results due to many components in the decomposition.