arXiv subjects

Tianju Xue

Publications and source records attributed to Tianju Xue.

15 recordsLinked to original sources

arXiv2026

TO-Master: an LLM-agent framework for automated topology optimization

Topology optimization (TO) has become a mature computational design method, but using it still requires substantial manual effort in geometry preparation, mesh generation, boundary-condition assignment, solver setup, and postprocessing. This implementation barrier limits the use of TO outside expert workflows, even when differentiable finite element solvers are available. This work introduces TO-Master, a large language model (LLM) agent framework that turns finite-element-based TO into a conversational, tool-orchestrated workflow. From natural language instructions and optional mesh, geometry, or image inputs, the agent selects computational tools, constructs finite element TO models, checks meshes and boundary conditions, and launches sensitivity-based optimization with typed solver arguments. The framework supports generated and uploaded meshes, image-to-mesh conversion, 2D and 3D structural compliance minimization, thermal conduction, multiple load cases, stress-constrained optimization, and engineering geometries. Numerical experiments show that TO-Master can reproduce standard benchmark results and solve more complex engineering examples while returning optimized results, field distributions, convergence histories, and interactive artifacts without user-written code. An instruction ablation study further shows that tool-usage rules, internal reasoning guidance, and few-shot examples are critical for robust formulation under ambiguous user input. By combining LLM-agent orchestration with deterministic finite element and optimization tools, TO-Master removes the burden of trivial setup and routine model construction, lowers the modeling barrier of TO, and preserves a reliable numerical workflow. The TO-Master platform is available online at https://www.bohrium.com/en/apps/to-master.

cs.CE↗

arXiv2026

Physics-guided diffusion models for inverse design of disordered metamaterials

Disordered metamaterials are promising for programming physical properties across diverse applications, yet their inverse design remains challenging due to the non-intuitive structure-property relationships and large design spaces. Recent generative approaches, particularly diffusion models, have shown potential in high-dimensional inverse design tasks. However, existing methods typically rely on carefully crafted training objectives, such as conditional data-driven or physics-informed loss functions. Because these strategies are inherently task-specific, the model must be retrained from scratch whenever the design problem changes (e.g., different governing equations, boundary conditions, or design objectives), severely limiting their flexibility and generalization ability. In this work, we propose physics-guided diffusion models that leverage differentiable physics-based solvers to instantly guide the generative process for inverse design. Drawing inspiration from classifier guidance, we develop a sampling strategy that directly incorporates physics guidance into the reverse stochastic differential equations. Our approach enables task-adaptive generation using gradients from differentiable solvers, while the diffusion model itself needs to be trained only once on unlabeled data. Focusing on disordered foam metamaterials, we present three representative design tasks: (1) achieving target effective thermal conductivity, (2) matching desired load-displacement response, and (3) maximizing energy absorption involving fractures. In each scenario, the proposed method successfully generates foam-like geometries that fulfill the prescribed physical objectives. These results demonstrate the versatility, efficiency, and practicality of physics-guided diffusion models for tackling complex inverse design problems in disordered metamaterials and beyond.

cs.CE↗

arXiv2026

Lattice Discrete Particle Model (LDPM): Comparison of Various Time Integration Solvers and Implementations

This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of transient implicit and explicit solvers and steady-state (static) solvers and implementations for Central Processing Unit (CPU) as well as Graphics Processing Unit (GPU). The various implementations are compared on the basis of a set of benchmarks tests describing behaviors of increasing computational complexity. They include elastic vibrations, confined strain-hardening compressive response, tensile fracture, and unconfined strain-softening compressive response. Metrics of interest extracted from the simulations include macroscopic stress versus strain responses, computational times, number of iterations, and energy balance error. Pairwise comparison of final crack patterns is provided through the correlation coefficient and normalized root mean square error of the crack opening vectors. Moreover, for the most numerically challenging case of unconfined compression with sliding boundary conditions, the stability of the strain-softening response is tested by perturbing the solutions as well as changing the convergence criteria and time step size. Attached to this paper is the complete input data of the benchmark tests; this will allow researchers to run the examples and compare them with their own implementations. In addition, most of the reported implementations are publicly available in open source packages.

cs.CE↗

arXiv2026

Style-constrained inverse design of microstructures with tailored mechanical properties using unconditional diffusion models

Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. Nevertheless, these recent methods typically rely on conditional training mechanisms and demand substantial computational effort to prepare the labeled training dataset, which makes them inflexible since any change in the governing equations or boundary conditions requires a complete retraining process. In this study, we propose a new inverse design framework that integrates unconditional denoising diffusion models with differentiable programming techniques for architected microstructure generation. Our approach eliminates the need for expensive labeled dataset preparation and retraining for different problem settings. By reinterpreting the noise input to the diffusion model as an optimizable design variable, we formulate the design task as an optimization problem over the noise input, enabling control over the reverse denoising trajectory to guide the generated microstructure toward the desired mechanical properties while preserving the stylistic constraints encoded in the training dataset. A unified differentiation pipeline via vector-Jacobian product concatenations is developed to enable end-to-end gradient evaluation through backpropagation. Several numerical examples, ranging from the design of microstructures with specified homogenized properties to those with targeted hyperelastic and elasto-plastic behaviors, showcase the effectiveness of the framework and its potential for advanced design tasks involving diverse performance and style requirements.

cs.CE↗

arXiv2025

Bohrium + SciMaster: Building the Infrastructure and Ecosystem for Agentic Science at Scale

AI agents are emerging as a practical way to run multi-step scientific workflows that interleave reasoning with tool use and verification, pointing to a shift from isolated AI-assisted steps toward \emph{agentic science at scale}. This shift is increasingly feasible, as scientific tools and models can be invoked through stable interfaces and verified with recorded execution traces, and increasingly necessary, as AI accelerates scientific output and stresses the peer-review and publication pipeline, raising the bar for traceability and credible evaluation. However, scaling agentic science remains difficult: workflows are hard to observe and reproduce; many tools and laboratory systems are not agent-ready; execution is hard to trace and govern; and prototype AI Scientist systems are often bespoke, limiting reuse and systematic improvement from real workflow signals. We argue that scaling agentic science requires an infrastructure-and-ecosystem approach, instantiated in Bohrium+SciMaster. Bohrium acts as a managed, traceable hub for AI4S assets -- akin to a HuggingFace of AI for Science -- that turns diverse scientific data, software, compute, and laboratory systems into agent-ready capabilities. SciMaster orchestrates these capabilities into long-horizon scientific workflows, on which scientific agents can be composed and executed. Between infrastructure and orchestration, a \emph{scientific intelligence substrate} organizes reusable models, knowledge, and components into executable building blocks for workflow reasoning and action, enabling composition, auditability, and improvement through use. We demonstrate this stack with eleven representative master agents in real workflows, achieving orders-of-magnitude reductions in end-to-end scientific cycle time and generating execution-grounded signals from real workloads at multi-million scale.

cs.AI↗

arXiv2025

Three-dimensional third medium contact model for hyperelastic contact and pneumatically actuated systems

This work presents a comprehensive three-dimensional third-medium contact framework for modeling complex contact interactions in hyperelastic solids and pneumatically actuated systems. The proposed third-medium formulation embeds a fictitious medium (or third medium) between potentially interacting bodies, enabling a unified and robust treatment of hyperelastic contact and self-contact without the need for discretization of the contact interface. Unlike the widely studied two-dimensional problem, this paper extends the new regularization term given in Reference \cite{TMCWriggers2} to three-dimensional problems and ensures element quality in a third medium. Due to the need for higher-order elements for the regularization term, this paper details the linearization process of this problem within the finite element framework. In addition, pneumatically actuated systems are considered by introducing a pneumatic term to represent pneumatic loading (pressure or suction) and inducing contact caused by internal inflation. This approach is suitable for complex hyperelastic contact and self-contact, and has potential applications in the fields of soft robotics and flexible mechanisms. The framework is developed in a fully three-dimensional setting, making it also suitable for isogeometric methods and meshless methods. Several benchmark and application-level simulations demonstrate the accuracy, robustness, and versatility of the proposed approach. The results highlight the capability of the three-dimensional third-medium model to handle challenging nonlinear contact scenarios relevant to soft materials, soft actuators, and emerging multifunctional structures.

math-ph↗

arXiv2025

Solving contact problems using Fiber Monte Carlo

Computational modeling of contact is fundamental to many engineering applications, yet accurately and efficiently solving complex contact problems remains challenging. In this work, we propose a new contact algorithm that computes contact forces by taking the gradient of an energy function of the contact volume (overlap) with respect to the geometry descriptors. While elegant in concept, evaluating this gradient is non-trivial due to the arbitrary geometry of the contact region. Inspired by the recently proposed Fiber Monte Carlo (FMC) method, we develop an algorithm that accurately computes contact forces based on the overlap volume between bodies with complex geometries. Our computational framework operates independently of mesh conformity, eliminating the need for master-slave identification and projection iterations, thus handling arbitrary discretizations. Moreover, by removing explicit complementarity constraints, the method retains a simple structure that can be easily incorporated into existing numerical solvers, such as the finite element method. In this paper, numerical examples cover a wide range of contact scenarios, from classical small-deformation static contact to complex large-deformation dynamic contact in both two- and three-dimensional settings with nonlinear material behavior. These cases include Hertzian contact for small-deformation verification; contact between wedge- and cone-shaped bodies to assess pressure and displacement predictions at non-smooth boundaries; contact involving Neo-Hookean hyperelastic materials for evaluating nonlinear responses under finite deformation; and dynamic collision cases to examine transient behavior.

cs.CE↗

arXiv2025

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics

Differentiable programming is revolutionizing computational science by enabling automatic differentiation (AD) of numerical simulations. While first-order gradients are well-established, second-order derivatives (Hessians) for implicit functions in finite-element-based differentiable physics remain underexplored. This work bridges this gap by deriving and implementing a framework for implicit Hessian computation in PDE-constrained optimization problems. We leverage primitive AD tools (Jacobian-vector product/vector-Jacobian product) to build an algorithm for Hessian-vector products and validate the accuracy against finite difference approximations. Four benchmarks spanning linear/nonlinear, 2D/3D, and single/coupled-variable problems demonstrate the utility of second-order information. Results show that the Newton-CG method with exact Hessians accelerates convergence for nonlinear inverse problems (e.g., traction force identification, shape optimization), while the L-BFGS-B method suffices for linear cases. Our work provides a robust foundation for integrating second-order implicit differentiation into differentiable physics engines, enabling faster and more reliable optimization.

cs.CE↗

arXiv2025

DiffLiB: High-fidelity differentiable modeling of lithium-ion batteries and efficient gradient-based parameter identification

The physics-based Doyle-Fuller-Newman (DFN) model, widely adopted for its precise electrochemical modeling, stands out among various simulation models of lithium-ion batteries (LIBs). Although the DFN model is powerful in forward predictive analysis, the inverse identification of its model parameters has remained a long-standing challenge. The numerous unknown parameters associated with the nonlinear, time-dependent, and multi-scale DFN model are extremely difficult to be determined accurately and efficiently, hindering the practical use of such battery simulation models in industrial applications. To tackle this challenge, we introduce DiffLiB, a high-fidelity finite-element-based LIB simulation framework, equipped with advanced differentiable programming techniques so that efficient gradient-based inverse parameter identification is enabled. Customized automatic differentiation rules are defined by identifying the VJP (vector-Jacobian product) structure in the chain rule and implemented using adjoint-based implicit differentiation methods. Four numerical examples, including both 2D and 3D forward predictions and inverse parameter identification, are presented to validate the accuracy and computational efficiency of DiffLiB. Benchmarking against COMSOL demonstrates excellent agreement in forward predictions, with terminal voltage discrepancies maintaining a root-mean-square error (RMSE) below 2 mV across all test conditions. In parameter identification tasks using experimentally measured voltage data, the proposed gradient-based optimization scheme achieves superior computational performance, with 96% fewer forward predictions and 72% less computational time compared with gradient-free approaches. These results demonstrate that DiffLiB is a versatile and powerful computational framework for the development of advanced LIBs.

cs.CE↗

arXiv2023

More Stiffness with Less Fiber: End-to-End Fiber Path Optimization for 3D-Printed Composites

In 3D printing, stiff fibers (e.g., carbon fiber) can reinforce thermoplastic polymers with limited stiffness. However, existing commercial digital manufacturing software only provides a few simple fiber layout algorithms, which solely use the geometry of the shape. In this work, we build an automated fiber path planning algorithm that maximizes the stiffness of a 3D print given specified external loads. We formalize this as an optimization problem: an objective function is designed to measure the stiffness of the object while regularizing certain properties of fiber paths (e.g., smoothness). To initialize each fiber path, we use finite element analysis to calculate the stress field on the object and greedily "walk" in the direction of the stress field. We then apply a gradient-based optimization algorithm that uses the adjoint method to calculate the gradient of stiffness with respect to fiber layout. We compare our approach, in both simulation and real-world experiments, to three baselines: (1) concentric fiber rings generated by Eiger, a leading digital manufacturing software package developed by Markforged, (2) greedy extraction on the simulated stress field (i.e., our method without optimization), and (3) the greedy algorithm on a fiber orientation field calculated by smoothing the simulated stress fields. The results show that objects with fiber paths generated by our algorithm achieve greater stiffness while using less fiber than the baselines--our algorithm improves the Pareto frontier of object stiffness as a function of fiber usage. Ablation studies show that the smoothing regularizer is needed for feasible fiber paths and stability of optimization, and multi-resolution optimization helps reduce the running time compared to single-resolution optimization.

cs.CE↗

arXiv2023

Hybrid thermal modeling of additive manufacturing processes using physics-informed neural networks for temperature prediction and parameter identification

Understanding the thermal behavior of additive manufacturing (AM) processes is crucial for enhancing the quality control and enabling customized process design. Most purely physics-based computational models suffer from intensive computational costs and the need of calibrating unknown parameters, thus not suitable for online control and iterative design application. Data-driven models taking advantage of the latest developed computational tools can serve as a more efficient surrogate, but they are usually trained over a large amount of simulation data and often fail to effectively use small but high-quality experimental data. In this work, we developed a hybrid physics-based data-driven thermal modeling approach of AM processes using physics-informed neural networks. Specifically, partially observed temperature data measured from an infrared camera is combined with the physics laws to predict full-field temperature history and to discover unknown material and process parameters. In the numerical and experimental examples, the effectiveness of adding auxiliary training data and using the pretrained model on training efficiency and prediction accuracy, as well as the ability to identify unknown parameters with partially observed data, are demonstrated. The results show that the hybrid thermal model can effectively identify unknown parameters and capture the full-field temperature accurately, and thus it has the potential to be used in iterative process design and real-time process control of AM.

cs.LG↗

arXiv2022

JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented with pure Python while scalable to efficiently solve problems with moderate to large sizes. For example, in a 3D tensile loading problem with 7.7 million degrees of freedom, JAX-FEM with GPU achieves around 10$\times$ acceleration compared to a commercial FEM code depending on platform. Beyond efficiently solving forward problems, JAX-FEM employs the automatic differentiation technique so that inverse problems are solved in a fully automatic manner without the need to manually derive sensitivities. Examples of 3D topology optimization of nonlinear materials are shown to achieve optimal compliance. Finally, JAX-FEM is an integrated platform for machine learning-aided computational mechanics. We show an example of data-driven multi-scale computations of a composite material where JAX-FEM provides an all-in-one solution from microscopic data generation and model training to macroscopic FE computations. The source code of the library and these examples are shared with the community to facilitate computational mechanics research.

cs.MS↗

arXiv2022

Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic responses of the continuum metamaterials. Yet it remains a challenge to accurately construct such systems based on the geometry of the building blocks of the metamaterial. In this work, we propose a machine learning approach to address this challenge. A metamaterial graph network (MGN) is used to represent the discrete system, where the nodal features contain the positions and orientations the rigid elements, and the edge update functions describe the mechanics of the nonlinear springs. We use Gaussian process regression as the surrogate model to characterize the elastic energy of the nonlinear springs as a function of the relative positions and orientations of the connected rigid elements. The optimal model can be obtained by "learning" from the data generated via finite element calculation over the corresponding building block of the continuum metamaterial. Then, we deploy the optimal model to the network so that the dynamics of the metamaterial at the structural scale can be studied. We verify the accuracy of our machine learning approach against several representative numerical examples. In these examples, the proposed approach can significantly reduce the computational cost when compared to direct numerical simulation while reaching comparable accuracy. Moreover, defects and spatial inhomogeneities can be easily incorporated into our approach, which can be useful for the rational design of soft mechanical metamaterials.

cs.CE↗

arXiv2021

Amortized Synthesis of Constrained Configurations Using a Differentiable Surrogate

In design, fabrication, and control problems, we are often faced with the task of synthesis, in which we must generate an object or configuration that satisfies a set of constraints while maximizing one or more objective functions. The synthesis problem is typically characterized by a physical process in which many different realizations may achieve the goal. This many-to-one map presents challenges to the supervised learning of feed-forward synthesis, as the set of viable designs may have a complex structure. In addition, the non-differentiable nature of many physical simulations prevents efficient direct optimization. We address both of these problems with a two-stage neural network architecture that we may consider to be an autoencoder. We first learn the decoder: a differentiable surrogate that approximates the many-to-one physical realization process. We then learn the encoder, which maps from goal to design, while using the fixed decoder to evaluate the quality of the realization. We evaluate the approach on two case studies: extruder path planning in additive manufacturing and constrained soft robot inverse kinematics. We compare our approach to direct optimization of the design using the learned surrogate, and to supervised learning of the synthesis problem. We find that our approach produces higher quality solutions than supervised learning, while being competitive in quality with direct optimization, at a greatly reduced computational cost.

cs.LG↗

arXiv2020

Learning Composable Energy Surrogates for PDE Order Reduction

Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs. To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system's total potential energy, which can be approximated by composing these surrogate models. Composable energy surrogates thus permit simulation in the reduced basis of component boundaries. Costly ground-truth simulation of the full structure is avoided, as training data are generated by performing finite element analysis with individual components. Using dataset aggregation to choose training boundary conditions allows us to learn energy surrogates which produce accurate macroscopic behavior when composed, accelerating simulation of parametric meta-materials.

cs.LG↗