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The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec’s simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.

 

We develop a set of highly efficient and effective computational algorithms and simulation tools for fluid simulations on a network. The mathematical models are a set of hyperbolic conservation laws on edges of a network, as well as coupling conditions on junctions of a network. For example, the shallow water system, together with flux balance and continuity conditions at river intersections, model water flows on a river network. The computationally accurate and robust discontinuous Galerkin methods, coupled with explicit strong stability preserving Runge-Kutta methods, are implemented for simulations on network edges. Meanwhile, linear and nonlinear scalable Riemann solvers are being developed and implemented at network vertices. These network simulations result in tools that are added to the existing PETSc and DMNetwork software libraries for the scientific community in general. Simulation results of a shallow water system on a Mississippi river network with over one billion network variables are performed on an extreme-scale computer using up to 8,192 processor with an optimal parallel efficiency. Further potential applications include traffic flow simulations on a highway network and blood flow simulations on a arterial network, among many others. 

The SNP-set analysis is a powerful tool for dissecting the genetics of complex human diseases. There are three fundamental genetic association approaches to SNR-set analysis: the marginal model fitting approach, the joint model fitting approach, and the decorrelation approach. A problem of primary interest is how these approaches compare with each other. To address this problem, we develop a theoretical platform to compare the signal-to-noise ratio (SNR) of these approaches under the generalized linear model. We elaborate on how causal genetic effects give rise to statistically detectable association signals, and show that when causal effects spread over blocks of strong linkage disequilibrium (LD), the SNR of the marginal model fitting is usually higher than that of the decorrelation approach, which in turn is higher than that of the unbiased joint model fitting approach. We also scrutinize dense effects and LDs by a bivariate model and extensive simulations using the 1000 Genome Project data. Last, we compare the statistical power of two generic types of SNP-set tests (summation-based and supremum-based) by simulations and an osteoporosis study using large data from UK Biobank. Our results help develop powerful tools for SNP-set analysis and understand the signal detection problem in the presence of colored noise. 

Digibox is a prototyping environment for IoT applications. It enables a novel scene-centric prototyping where developers can program an ensemble of simulated devices to capture not only their individual but also their coordinated behaviors, making it possible to test, debug, and evaluate the behaviors of an IoT application. Using Digibox, developers can download and reuse existing scenes, customize, and repurpose them towards developing new applications; or replicate others' experiment results from scientific research. Digibox's Kubernetes-based runtime further allows developers to easily scale the prototyping environment from a single laptop to a cluster running simulated devices and scenes at a scale appropriate to the application. 

Combining SNP p -values from GWAS summary data is a promising strategy for detecting novel genetic factors. Existing statistical methods for the p -value-based SNP-set testing confront two challenges. First, the statistical power of different methods depends on unknown patterns of genetic effects that could drastically vary over different SNP sets. Second, they do not identify which SNPs primarily contribute to the global association of the whole set. We propose a new signal-adaptive analysis pipeline to address these challenges using the omnibus thresholding Fisher’s method (oTFisher). The oTFisher remains robustly powerful over various patterns of genetic effects. Its adaptive thresholding can be applied to estimate important SNPs contributing to the overall significance of the given SNP set. We develop efficient calculation algorithms to control the type I error rate, which accounts for the linkage disequilibrium among SNPs. Extensive simulations show that the oTFisher has robustly high power and provides a higher balanced accuracy in screening SNPs than the traditional Bonferroni and FDR procedures. We applied the oTFisher to study the genetic association of genes and haplotype blocks of the bone density-related traits using the summary data of the Genetic Factors for Osteoporosis Consortium. The oTFisher identified more novel and literature-reported genetic factors than existing p -value combination methods. Relevant computation has been implemented into the R package TFisher to support similar data analysis. 

The chemical composition of the deep continental crust is key to understanding the formation and evolution of the continental crust. Constraining the chemical composition of present‐day deep continental crust is, however, limited by indirect accessibility. This paper presents a modeling method for constraining deep crustal chemical structures from observed crustal seismic structures. We compiled a set of published composition models for the continental crust to construct functional relationships between seismic wave speed and major oxide content in the crust. Phase equilibria and compressional wave speeds (V_P) for each composition model were calculated over a range of depths and temperatures of the deep crust. For conditions within the alpha(α)‐quartz stability field, robust functional relationships were obtained betweenV_Pand major oxide contents of the crust. Based on these relationships, observedV_Pof the deep crust can be inverted to chemical compositions for regions with given geotherms. We provide a MATLAB code for this process (CalcCrustComp). We apply this method to constrain compositions from deep crustalV_Pof global typical tectonic settings and the North China Craton (NCC). Our modeling results suggest that the lower crust in subduction‐related and rifting‐related tectonic settings may be more mafic than platforms/shields and orogens. The lowV_Psignature in the deep crust of the NCC can be explained by intermediate crustal compositions, higher water contents, and/or higher temperatures. The chemical structure obtained by this method can serve as a reference model to further identify deep crustal features.