Data-driven models are rising as an auspicious method for the geometrical design of materials and structural systems. Nevertheless, existing data-driven models customarily address the optimization of ...structural designs rather than metamaterial designs. Metamaterials are emerging as promising materials exhibiting tailorable and unprecedented properties for a wide spectrum of applications. In this paper, we develop a deep learning (DL) model based on a convolutional neural network (CNN) that predicts optimal metamaterial designs. The developed DL model non-iteratively optimizes metamaterials for either maximizing the bulk modulus, maximizing the shear modulus, or minimizing the Poisson's ratio (including negative values). The data are generated by solving a large set of inverse homogenization boundary values problems, with randomly generated geometrical features from a specific distribution. Such s data-driven model can play a vital role in accelerating more computationally expensive design problems, such as multiscale metamaterial systems.
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•A deep learning (DL) model is developed for obtaining optimized metamaterials.•The DL model optimizes for bulk modulus, shear modulus, or Poisson's ratio.•Parallel computing on the HPC system is used to generate the data needed for the DL model training.•The developed DL model shows high accuracy.
High performance computing is absolutely necessary for large-scale geophysical simulations. In order to obtain a realistic image of a geologically complex area, industrial surveys collect vast ...amounts of data making the computational cost extremely high for the subsequent simulations. A major computational bottleneck of modeling and inversion algorithms is solving the large sparse systems of linear ill-conditioned equations in complex domains with multiple right hand sides. Recently, parallel direct solvers have been successfully applied to multi-source seismic and electromagnetic problems. These methods are robust and exhibit good performance, but often require large amounts of memory and have limited scalability. In this paper, we evaluate modern direct solvers on large-scale modeling examples that previously were considered unachievable with these methods. Performance and scalability tests utilizing up to 65,536 cores on the Blue Waters supercomputer clearly illustrate the robustness, efficiency and competitiveness of direct solvers compared to iterative techniques. Wide use of direct methods utilizing modern parallel architectures will allow modeling tools to accurately support multi-source surveys and 3D data acquisition geometries, thus promoting a more efficient use of the electromagnetic methods in geophysics.
•Parallel direct solvers are evaluated on large problems of electromagnetic modeling.•Performance and memory requirements are compared on different architectures.•Robustness and efficiency of direct solvers for multi-source problems is confirmed.•Scalability tests utilizing up to 65,536 cores are presented.
The solidifying steel follows highly nonlinear thermo-mechanical behavior depending on the loading history, temperature, and metallurgical phase fraction calculations (liquid, ferrite, and ...austenite). Numerical modeling with a computationally challenging multiphysics approach is used on high-performance computing to generate sufficient training and testing data for subsequent deep learning. We have demonstrated how the innovative sequence deep learning methods can learn from multiphysics modeling data of a solidifying slice traveling in a continuous caster and correctly and instantly capture the complex history and temperature-dependent phenomenon in test data samples never seen by the deep learning networks.
This article introduces a computational design framework for obtaining three‐dimensional (3D) periodic elastoplastic architected materials with enhanced performance, subject to uniaxial or shear ...strain. A nonlinear finite element model accounting for plastic deformation is developed, where a Lagrange multiplier approach is utilized to impose periodicity constraints. The analysis assumes that the material obeys a von Mises plasticity model with linear isotropic hardening. The finite element model is combined with a corresponding path‐dependent adjoint sensitivity formulation, which is derived analytically. The optimization problem is parametrized using the solid isotropic material penalization method. Designs are optimized for either end compliance or toughness for a given prescribed displacement. Such a framework results in producing materials with enhanced performance through much better utilization of an elastoplastic material. Several 3D examples are used to demonstrate the effectiveness of the mathematical framework.
Two thermo-mechanical models based on different elastic-visco-plastic constitutive laws are applied to simulate temperature and stress development of a slice through the solidifying shell of 0.27%C ...steel in a continuous casting mold under typical commercial operating conditions with realistic temperature dependant properties. A general form of the transient heat equation, including latent-heat from phase transformations such as solidification and other temperature-dependent properties, is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the elastic-visco-plastic constitutive laws of Kozlowski P.F. Kozlowski, B.G. Thomas, J.A. Azzi, H. Wang, Simple constitutive equations for steel at high temperature, Metall. Trans. 23A (1992) 903–918 for austenite in combination with the Zhu power-law H. Zhu, Coupled thermal–mechanical finite-element model with application to initial solidification, PhD thesis, University of Illinois, 1993 for delta-ferrite with ABAQUS ABAQUS Inc., User Manuals v6.6, 2006 using a user-defined subroutine UMAT S. Koric, B.G. Thomas, Efficient thermo-mechanical model for solidification processes, Int. J. Num. Meth. Eng. 66 (2006) 1955–1989, and the Anand law for steel L. Anand, Constitutive equations for the rate dependant deformation of metals at elevated temperatures, ASME J. Eng. Mater. Technol. 104 (1982) 12–17; S.B. Brown, K.H. Kim, L. Anand, An internal variable constitutive model for hot working of metals, Int. J. Plasticity 6 (1989) 95–130 using the integration scheme recently implemented in ANSYS ANSYS Inc., User Manuals v100, 2006. The results from these two approaches are compared and CPU times are benchmarked. A comparison of one-dimensional constitutive behavior of these laws with experimental tensile test data P.J. Wray, Plastic deformation of delta-ferritic iron at intermediate strain rates, Metall. Trans. A 7A (1976) 1621–1627; P.J. Wray, Effect of carbon content on the plastic flow of plain carbon steel at elevated temperatures, Metall. Trans. A 13 (1982) 125–134 and previous work A.E. Huespe, A. Cardona, N. Nigro, V. Fachinotti, Visco-plastic constitutive models of steel at high temperature, J. Mater. Process. Technol. 102 (2000) 143–152 shows reasonable agreement for both models, although the Kozlowski–Zhu approach is much more accurate for low carbon steels. The thermo-mechanical models studied here are useful for efficient and accurate analysis of steel solidification processes using convenient commercial software.
•Data-driven and physics-informed Deep Learning Operator Networks (DeepONets) are devised to learn the solution operator of the Heat (Poisson's) Conduction equation with a parametric spatially ...multi-dimensional heat source.•We have provided novel computational insights into the DeepONet learning process of temperature solution with spatially multi-dimensional parametric input.•Once Data-driven and physics-informed DeepONets learn to solve the Heat Conduction equation, they can instantly inference accurate temperature solutions for a new parametric source distribution without re-training or transfer learning.•Many challenging and iterative engineering and scientific computations governed by parametric PDEs will benefit from similar DeepONet-based surrogate deep learning models.
Deep neural networks as universal approximators of partial differential equations (PDEs) have attracted attention in numerous scientific and technical circles with the introduction of Physics-informed Neural Networks (PINNs). However, in most existing approaches, PINN can only provide solutions for defined input parameters, such as source terms, loads, boundaries, and initial conditions. Any modification in such parameters necessitates retraining or transfer learning. Classical numerical techniques are no exception, as each new input parameter value necessitates a new independent simulation. Unlike PINNs, which approximate solution functions, DeepONet approximates linear and nonlinear PDE solution operators by using parametric functions (infinite-dimensional objects) as inputs and mapping them to different PDE solution function output spaces. We devise, apply, and compare data-driven and physics-informed DeepONet models to solve the heat conduction (Poisson's) equation, one of the most common PDEs in science and engineering, using the variable and spatially multi-dimensional source term as its parameter. We provide novel computational insights into the DeepONet learning process of PDE solution with spatially multi-dimensional parametric input functions. We also show that, after being adequately trained, the proposed frameworks can reliably and almost instantly predict the parametric solution while being orders of magnitude faster than classical numerical solvers and without any additional training.
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Significant investments to upgrade and construct large-scale scientific facilities demand commensurate investments in R&D to design algorithms and computing approaches to enable scientific and ...engineering breakthroughs in the big data era. Innovative Artificial Intelligence (AI) applications have powered transformational solutions for big data challenges in industry and technology that now drive a multi-billion dollar industry, and which play an ever increasing role shaping human social patterns. As AI continues to evolve into a computing paradigm endowed with statistical and mathematical rigor, it has become apparent that single-GPU solutions for training, validation, and testing are no longer sufficient for computational grand challenges brought about by scientific facilities that produce data at a rate and volume that outstrip the computing capabilities of available cyberinfrastructure platforms. This realization has been driving the confluence of AI and high performance computing (HPC) to reduce time-to-insight, and to enable a systematic study of domain-inspired AI architectures and optimization schemes to enable data-driven discovery. In this article we present a summary of recent developments in this field, and describe specific advances that authors in this article are spearheading to accelerate and streamline the use of HPC platforms to design and apply accelerated AI algorithms in academia and industry.
Using recent advancements in high-performance computing data assimilation to combine satellite InSAR data with numerical models, the prolonged unrest of the Sierra Negra volcano in the Galápagos was ...tracked to provide a fortuitous, but successful, forecast 5 months in advance of the 26 June 2018 eruption. Subsequent numerical simulations reveal that the evolution of the stress state in the host rock surrounding the Sierra Negra magma system likely controlled eruption timing. While changes in magma reservoir pressure remained modest (<15 MPa), modeled widespread Mohr-Coulomb failure is coincident with the timing of the 26 June 2018 moment magnitude 5.4 earthquake and subsequent eruption. Coulomb stress transfer models suggest that the faulting event triggered the 2018 eruption by encouraging tensile failure along the northern portion of the caldera. These findings provide a critical framework for understanding Sierra Negra's eruption cycles and evaluating the potential and timing of future eruptions.
Deep learning (DL) and the collocation method are merged and used to solve partial differential equations (PDEs) describing structures' deformation. We have considered different types of materials: ...linear elasticity, hyperelasticity (neo‐Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening. The performance of this deep collocation method (DCM) depends on the architecture of the neural network and the corresponding hyperparameters. The presented DCM is meshfree and avoids any spatial discretization, which is usually needed for the finite element method (FEM). We show that the DCM can capture the response qualitatively and quantitatively, without the need for any data generation using other numerical methods such as the FEM. Data generation usually is the main bottleneck in most data‐driven models. The DL model is trained to learn the model's parameters yielding accurate approximate solutions. Once the model is properly trained, solutions can be obtained almost instantly at any point in the domain, given its spatial coordinates. Therefore, the DCM is potentially a promising standalone technique to solve PDEs involved in the deformation of materials and structural systems as well as other physical phenomena.
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