Partial differential equations (PDEs) are fundamental to modeling complex and nonlinear physical phenomena, but their numerical solution often requires significant computational resources, particularly when a large number of forward full solution evaluations are necessary, such as in design, optimization, sensitivity analysis, and uncertainty quantification. Recent advances in artificial intelligence – particularly operator learning – have enabled surrogate models that efficiently predict full-field PDE solutions; however, these models often struggle with accuracy and robustness when faced with highly nonlinear responses driven by sequential input functions. To address these challenges, we propose the Sequential Neural Operator Transformer (S-NOT), an architecture that combines gated recurrent units (GRUs) with the self-attention mechanism of transformers to address time-dependent, nonlinear PDEs. Unlike sequential-deep operator networks(S-DON), which use a dot product to merge encoded outputs from the branch and trunk sub-networks, S-NOT leverages attention to better capture intricate dependencies between sequential inputs and spatial query points. We benchmark S-NOT on three challenging datasets from real-world applications with plastic and thermo-viscoplastic highly nonlinear material responses: multiphysics steel solidification, a three dimensional (3D) lug specimen, and a dogbone specimen under temporal and path-dependent loadings. The results show that S-NOT yields prediction errors up to 4.5 times smaller than S-DON even for data outliers. Furthermore, S-NOT provides an acceleration of 4 orders-of-magnitude compared to traditional finite element method simulations, demonstrating its accuracy and robustness for drastically accelerating computational frameworks in scientific and engineering applications.

Metamaterials, synthetic materials with customized properties, have emerged as a promising field due to advancements in additive manufacturing. These materials derive unique mechanical properties from their internal lattice structures, which are often composed of multiple materials that repeat geometric patterns. While traditional inverse design approaches have shown potential, they struggle to map nonlinear material behavior to multiple possible structural configurations. This paper presents a novel framework leveraging video diffusion models, a type of generative Artificial Intelligence (AI), for inverse multi-material design based on nonlinear stress–strain responses. Our approach consists of two key components: (1) a fields generator using a video diffusion model to create solution fields based on target nonlinear stress–strain responses, and (2) a structure identifier employing two U-shaped encoder–decoder network (UNet) architectures to determine the corresponding multi-material two-dimensional (2D) design. By incorporating multiple materials, plasticity, contact, and large deformation, our innovative design method allows for enhanced control over the highly nonlinear mechanical behavior of metamaterials commonly seen in real-world applications within 10% relative error from desired property. It offers a promising solution for generating next-generation metamaterials with finely tuned mechanical characteristics.

A state-of-the-art large eddy simulation code has been developed to solve compressible flows in turbomachinery. The code has been engineered with a high degree of scalability, enabling it to effectively leverage the many-core architecture of the new Sunway system. A consistent performance of 115.8 DP-PFLOPs has been achieved on a high-pressure turbine cascade consisting of over 1.69 billion mesh elements and 865 billion Degree of Freedoms (DOFs). By leveraging a high-order unstructured solver and its portability to large heterogeneous parallel systems, we have progressed towards solving the grand challenge problem outlined by NASA [1], which involves a time-dependent simulation of a complete engine, incorporating all the aerodynamic and heat transfer components.

LS-DYNA is a well-known multiphysics code with both explicit and implicit time stepping capabilities. Implicit simulations rely heavily on sparse matrix computations, in particular direct solvers, and are notoriously much harder to scale than explicit simulations. In this paper, we investigate the scalability challenges of the implicit structural mode of LS- DYNA. In particular, we focus on linear constraint analysis, sparse matrix reordering, symbolic factorization, and numerical factorization. Our problem of choice for this study is a thermomechanical simulation of jet engine models built by Rolls-Royce with up to 200 million degrees of freedom, or equations. The models are used for engine performance analysis and design optimization, in particular optimization of tip clearances in the compressor and turbine sections of the engine. We present results using as many as 131,072 cores on the Blue Waters Cray XE6/XK7 supercomputer at NCSA and the Titan Cray XK7 supercomputer at OLCF. Since the main focus is on general linear algebra problems, this work is of interest for all linear algebra practitioners, not only developers of implicit finite element codes.

Direct methods for solving sparse systems of linear equations have a high asymptotic computational and memory requirements relative to iterative methods. However, systems arising in some applications, such as structural analysis, can often be too ill-conditioned for iterative solvers to be effective. We cite real applications where this is indeed the case, and using matrices extracted from these applications to conduct experiments on three different massively parallel architectures, show that a well designed sparse factorization algorithm can attain very high levels of performance and scalability. We present strong scalability results for test data from real applications on up to 8,192 cores, along with both analytical and experimental weak scalability results for a model problem on up to 16,384 cores---an unprecedented number for sparse factorization. For the model problem, we also compare experimental results with multiple analytical scaling metrics and distinguish between some commonly used weak scaling methods.