arXiv subjects

Jiachen Guo

Publications and source records attributed to Jiachen Guo.

At least 19 recordsLinked to original sources

arXiv2026

From Feature Interaction to Feature Transport - A Unified Block for Scalable Recommendation Models

Unified recommendation models aim to jointly model non-sequential multi-field features and sequential user behaviors, but existing interaction-centric designs mainly focus on mixing heterogeneous tokens within each layer. We argue that scalable unified recommendation also requires controlling how intent information is carried, filtered, and preserved across stacked blocks. Inspired by flow-based representation dynamics, we introduce feature transport, a view that treats deep unified recommendation as a discrete context-conditioned representation evolution process. We propose CRAFT, a Contextual Residual Adaptive Feature Transport block, which summarizes non-sequential features into a reliability-aware contextual field and uses it to generate residual displacement and memory-preserving signals for intent and sequence representations. In this way, non-sequential context acts as an active controller of representation evolution rather than a passive object of interaction. In the TAAC2026 advertising recommendation competition, CRAFT achieves a test AUC of 0.838090, surpassing the previous leaderboard-best score of 0.83798. Scaling experiments further show that CRAFT benefits from both depth and width expansion: stacking CRAFT to six blocks improves test AUC to 0.838148, while increasing the hidden dimension reaches 0.838106. These results demonstrate the effectiveness, scalability, and generalization potential of the feature transport paradigm. Source code: https://github.com/AshleyLuo001/CRAFT

cs.IR↗

arXiv2026

Geometry-Preserving Reduced-Order Modeling via Immersed Tensor Decomposition (ITD)

Body-fitted finite-element methods deliver high-order accuracy but hinge on a clean, watertight, conforming mesh, a requirement that breaks down for the geometrically imperfect CAD assemblies, image-based volumetric data, and voxel-native designs that pervade biomedical engineering and additive manufacturing, where mesh generation has become the dominant cost of the analysis cycle. Immersed methods on regular background Cartesian grids sidestep body-fitted meshing, but classical implementations integrate over irregular cut subdomains, destroying the tensor-product structure that enables separable, reduced-order methods such as tensor decomposition. In this paper we propose the \emph{Immersed Tensor Decomposition} (ITD) framework, which couples a mesh-free geometric representation via body-fitted function with the separable C-HiDeNN-TD reduced-order solver to enable large-scale simulation directly on regular background voxel meshes. The geometry is encoded in three steps: a signed-distance function represents the boundary, a body-fitted function $\Phi$ approximates it with controllable error, and a low-rank Tucker decomposition provides model-order reduction; for a fixed grid spacing $h$, accuracy is improved by raising the approximation order of C-HiDeNN interpolation up to degree $p$ with a linear background mesh. The central contribution is an exact Dirichlet formulation that enforces the boundary condition strongly by multiplying the trial function with $\Phi$, so that $u=g$ holds by construction without any variational penalty or interface quadrature. We establish an a priori error estimate for the formulation and assess it on canonical 2D/3D domains, demonstrating optimal convergence and robustness on non-Cartesian geometries discretized by regular voxel meshes.

math.NA↗

arXiv2026

Laser Powder Bed Fusion Melt Pool Dynamics for Different Geometric Variations and Powder Layer Heights: High-Fidelity Multiphysics Modeling vs 2025 NIST Experiments

Metal Laser Powder Bed Fusion (PBF-LB/M) is a leading additive manufacturing technique in which part quality and grain morphology are highly dependent on process parameters. Numerous studies of process variations, such as laser power, scan speed, and spot diameter, have demonstrated that they strongly influence melt pool dynamics; however, the effects of powder layer height and geometric variations remain less well understood. In this article, we focus on variations in powder layer height and part geometry to study their influence on melt pool dynamics. We employed a high-fidelity multiphysics simulation framework based on the open source finite volume method (FVM) solver package `LaserBeamFoam' built on `OpenFOAM' to study the variations in different melt pool metrics -- melt pool depth, width, bead height, overlap depth, overlap width, solidified area, and dilution area. The solver captures coupled phenomena of heat transfer, fluid flow, vaporization, recoil pressure, Marangoni convection, and realistic laser reflection behavior to accurately model the melt pool dynamics. Simulations are performed for different powder layer heights and geometric dimensions for direct comparison with benchmark experiments conducted at the National Institute of Standards and Technology (NIST) in 2025. Quantitative validation against NIST experiment demonstrates excellent agreement in all the melt pool metrics. These results highlight the predictive capability of physics-based PBF-LB models, paving the way for process optimization, defect mitigation, and the integration of simulation into digital twin frameworks for additive manufacturing.

physics.app-ph↗

arXiv2026

Bayesian Interpolating Neural Network (B-INN): a scalable and reliable Bayesian model for large-scale physical systems

Neural networks and machine learning models for uncertainty quantification suffer from limited scalability and poor reliability compared to their deterministic counterparts. In industry-scale active learning settings, where generating a single high-fidelity simulation may require days or weeks of computation and produce data volumes on the order of gigabytes, they quickly become impractical. This paper proposes a scalable and reliable Bayesian surrogate model, termed the Bayesian Interpolating Neural Network (B-INN). The B-INN combines high-order interpolation theory with tensor decomposition and alternating direction algorithm to enable effective dimensionality reduction without compromising predictive accuracy. We theoretically show that the function space of a B-INN is a subset of that of Gaussian processes, while its Bayesian inference exhibits linear complexity, $\mathcal{O}(N)$, with respect to the number of training samples. Numerical experiments demonstrate that B-INNs can be from 20 times to 10,000 times faster with a robust uncertainty estimation compared to Bayesian neural networks and Gaussian processes. These capabilities make B-INN a practical foundation for uncertainty-driven active learning in large-scale industrial simulations, where computational efficiency and robust uncertainty calibration are paramount.

math.NA↗

arXiv2026

CM-GAI: Continuum Mechanistic Generative Artificial Intelligence Theory for Data Dynamics

Generative artificial intelligence (GAI) plays a fundamental role in high-impact AI-based systems such as SORA and AlphaFold. Currently, GAI shows limited capability in the specialized domains due to data scarcity. In this paper, we develop a continuum mechanics-based theoretical framework to generalize the optimal transport theory from pure mathematics, which can be used to describe the dynamics of data, realizing the generative tasks with a small amount of data. The developed theory is used to solve three typical problem involved in many mechanical designs and engineering applications: at material level, how to generate the stress-strain response outside the range of experimental conditions based on experimentally measured stress-strain data; at structure level, how to generate the temperature-dependent stress fields under the thermal loading; at system level, how to generate the plastic strain fields under transient dynamic loading. Our results show the proposed theory can complete the generation successfully, showing its potential to solve many difficult problems involved in engineering applications, not limited to mechanics problems, such as image generation. The present work shows that mechanics can provide new tools for computer science. The limitation of the proposed theory is also discussed.

cs.CE↗

arXiv2025

Efficient GPU-computing simulation platform JAX-PF for differentiable phase field model

We present JAX-PF, an open-source, GPU-accelerated, and differentiable Phase Field (PF) software package, supporting both explicit and implicit time stepping schemes. Leveraging the modern computing architecture JAX, JAX-PF achieves high performance through array programming and GPU acceleration, delivering ~5x speedup over PRISMS-PF with MPI (24 CPU cores) for systems with ~4.19 million degrees of freedom using explicit schemes, and scaling efficiently with implicit schemes for large-size problems. Furthermore, a key feature of JAX-PF is automatic differentiation (AD), eliminating manual derivations of free-energy functionals and Jacobians. Beyond forward simulations, JAX-PF demonstrates its potential in inverse design by providing sensitivities for gradient-based optimization. We demonstrate, for the first time, the calibration of PF material parameters using AD-based sensitivities, highlighting its capability for high-dimensional inverse problems. By combining efficiency, flexibility, and full differentiability, JAX-PF offers a fast, practical, and integrated tool for forward simulation and inverse design, advancing co-designing of material and manufacturing processes and supporting the goals of the Materials Genome Initiative.

physics.comp-ph↗

arXiv2025

A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element Analysis

We present a framework for the Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) tailored for nonlinear finite element analysis. Building upon the structured foundation of HiDeNN, C-HiDeNN introduces a convolution operator to enhance numerical approximation. A distinctive feature of C-HiDeNN is its higher-order accurate approximation achieved through an expanded set of parameters, such as the polynomial order 'p,' dilation parameter 'a,' patch size 's,' and nodal position 'X'. These parameters function as the functional equivalents of weights and biases within each C-HiDeNN patch. In addition, C-HiDeNN can be selectively applied to regions requiring high resolution to adaptively improve local prediction accuracy. To demonstrate the effectiveness of this framework, we provide numerical examples in the context of nonlinear finite element analysis. The results show that our approach achieves significantly higher accuracy than conventional Finite Element Method (FEM) while substantially reducing computational costs.

math.NA↗

arXiv2025

Convolutional Hierarchical Deep Learning Neural Networks-Tensor Decomposition (C-HiDeNN-TD): a scalable surrogate modeling approach for large-scale physical systems

A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods based on artificial intelligence have been extensively investigated to accelerate partial differential equations (PDE) solvers using data-driven surrogates. However, most data-driven surrogates require an extremely large amount of training data. In this paper, we propose the Convolutional Hierarchical Deep Learning Neural Network-Tensor Decomposition (C-HiDeNN-TD) method, which can directly obtain surrogate models by solving large-scale space-time PDE without generating any offline training data. We compare the performance of the proposed method against classical numerical methods for extremely large-scale systems.

cs.CE↗

arXiv2025

MultiLevel Variational MultiScale (ML-VMS) framework for large-scale simulation

In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolutional Hierarchical Deep Neural Network (C-HiDeNN) as the approximation basis. The framework employs a coarse mesh throughout the domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order $p$, patch size $s$) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with $10^{10}$ spatial degrees of freedom (DoFs), our 3-level ML-VMS C-HiDeNN-TD achieves an approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM.

math.NA↗

arXiv2025

Large language model-empowered next-generation computer-aided engineering

Software development has entered a new era where large language models (LLMs) now serve as general-purpose reasoning engines, enabling natural language interaction and transformative applications across diverse domains. This paradigm is now extending into computer-aided engineering (CAE). Recent applications of LLMs in CAE have successfully automated routine tasks, including CAD model generation and FEM simulations. Nevertheless, these contributions, which primarily serve to reduce manual labor, are often insufficient for addressing the significant computational challenges posed by large-scale, high-dimensional systems. To this aim, we first introduce the concept of LLM-empowered CAE agent, where LLMs act as autonomous collaborators that plan, execute, and adapt CAE workflows. Then, we propose an LLM-empowered CAE agent for data-free model order reduction (MOR), a powerful yet underused approach for ultra-fast large-scale parametric analysis due to the intrusive nature and labor-intensive redevelopment of solvers. LLMs can alleviate this barrier by automating derivations, code restructuring, and implementation, making intrusive MOR both practical and broadly accessible. To demonstrate feasibility, we present an LLM-empowered CAE agent for solving ultra-large-scale space-parameter-time (S-P-T) physical problems using Tensor-decomposition-based A Priori Surrogates (TAPS). Our results show that natural language prompts describing parametric partial differential equations (PDEs) can be translated into efficient solver implementations, substantially reducing human effort while producing high-fidelity reduced-order models. Moreover, LLMs can synthesize novel MOR solvers for unseen cases such as nonlinear and high-dimensional parametric problems based on their internal knowledge base. This highlights the potential of LLMs to establish the foundation for next-generation CAE systems.

cs.CE↗

arXiv2025

Interpolating Neural Network-Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand prohibitively large computational resources and yield limited accuracy when scaling to large-scale, high-dimensional physical problems. Their black-box nature further hinders the application in industrial problems where interpretability and high precision are critical. To overcome these challenges, this paper introduces Interpolating Neural Network-Tensor Decomposition (INN-TD), a scalable and interpretable framework that has the merits of both machine learning and finite element methods for modeling large-scale physical systems. By integrating locally supported interpolation functions from finite element into the network architecture, INN-TD achieves a sparse learning structure with enhanced accuracy, faster training/solving speed, and reduced memory footprint. This makes it particularly effective for tackling large-scale high-dimensional parametric PDEs in training, solving, and inverse optimization tasks in physical problems where high precision is required.

cs.CE↗

arXiv2025

Tensor-decomposition-based A Priori Surrogate (TAPS) modeling for ultra large-scale simulations

A data-free, predictive scientific AI model, Tensor-decomposition-based A Priori Surrogate (TAPS), is proposed for tackling ultra large-scale engineering simulations with significant speedup, memory savings, and storage gain. TAPS can effectively obtain surrogate models for high-dimensional parametric problems with equivalent zetta-scale ($10^{21}$) degrees of freedom (DoFs). TAPS achieves this by directly obtaining reduced-order models through solving governing equations with multiple independent variables such as spatial coordinates, parameters, and time. The paper first introduces an AI-enhanced finite element-type interpolation function called convolution hierarchical deep-learning neural network (C-HiDeNN) with tensor decomposition (TD). Subsequently, the generalized space-parameter-time Galerkin weak form and the corresponding matrix form are derived. Through the choice of TAPS hyperparameters, an arbitrary convergence rate can be achieved. To show the capabilities of this framework, TAPS is then used to simulate a large-scale additive manufacturing process as an example and achieves around 1,370x speedup, 14.8x memory savings, and 955x storage gain compared to the finite difference method with $3.46$ billion spatial degrees of freedom (DoFs). As a result, the TAPS framework opens a new avenue for many challenging ultra large-scale engineering problems, such as additive manufacturing and integrated circuit design, among others.

cs.CE↗

arXiv2025

Superstring amplitudes from BCJ numerators at one loop

We find a direct map that determines moduli-space integrands for one-loop superstring amplitudes in terms of field-theory loop integrands in the BCJ form. The latter can be computed using efficient unitarity methods, so our map provides an alternative to worldsheet CFT techniques. This construction is a one-loop higher-point analogue of a recent conjecture for the three-loop four-point superstring amplitude. Based on the one-loop chiral-splitting representation, we show how all coefficients of an ansatz for the superstring can be identified with field-theory BCJ numerators, up to at least 7-point amplitudes. Moreover, we obtain partial results for all higher-point amplitudes. The monodromy constraints associated to chiral splitting play a crucial role in determining coefficients of the ansatz that, naively, are not fixed by the field-theory limit. Taking a field-theory perspective, our ansatz for the superstring implies by construction the existence of one-loop BCJ numerators at any multiplicity.

hep-th↗

arXiv2024

Interpolating neural network: A novel unification of machine learning and interpolation theory

Artificial intelligence (AI) has revolutionized software development, shifting from task-specific codes (Software 1.0) to neural network-based approaches (Software 2.0). However, applying this transition in engineering software presents challenges, including low surrogate model accuracy, the curse of dimensionality in inverse design, and rising complexity in physical simulations. We introduce an interpolating neural network (INN), grounded in interpolation theory and tensor decomposition, to realize Engineering Software 2.0 by advancing data training, partial differential equation solving, and parameter calibration. INN offers orders of magnitude fewer trainable/solvable parameters for comparable model accuracy than traditional multi-layer perceptron (MLP) or physics-informed neural networks (PINN). Demonstrated in metal additive manufacturing, INN rapidly constructs an accurate surrogate model of Laser Powder Bed Fusion (L-PBF) heat transfer simulation, achieving sub-10-micrometer resolution for a 10 mm path in under 15 minutes on a single GPU. This makes a transformative step forward across all domains essential to engineering software.

cs.LG↗

arXiv2024

Decade-Bandwidth RF-Input Pseudo-Doherty Load Modulated Balanced Amplifier using Signal-Flow-Based Phase Alignment Design

This paper reports a first-ever decade-bandwidth pseudo-Doherty load-modulated balanced amplifier (PD-LMBA), designed for emerging 4G/5G communications and multi-band operations. By revisiting the LMBA theory using the signal-flow graph, a frequency-agnostic phase-alignment condition is found that is critical for ensuring intrinsically broadband load modulation behavior. This unique design methodology enables, for the first time, the independent optimization of broadband balanced amplifier (BA, as the peaking) and control amplifier (CA, as the carrier), thus fundamentally addressing the longstanding limits imposed on the design of wideband load-modulated power amplifiers (PAs). To prove the proposed concept, an ultra-wideband RF-input PD-LMBA is designed and developed using GaN technology covering the frequency range from 0.2 to 2 GHz. Experimental results demonstrate an efficiency of 51% to 72% for peak output power and 44% to 62% for 10-dB OBO, respectively.

cs.AR↗

arXiv2024

Linear Hybrid Asymmetrical Load-Modulated Balanced Amplifier with Multi-Band Reconfigurability and Antenna-VSWR Resilience

This paper presents the first-ever highly linear and load-insensitive three-way load-modulation power amplifier (PA) based on reconfigurable hybrid asymmetrical load modulated balanced amplifier (H-ALMBA). Through proper amplitude and phase controls, the carrier, control amplifier (CA), and two peaking balanced amplifiers (BA1 and BA2) can form a linear high-order load modulation over wide bandwidth. Moreover, it is theoretically unveiled that the load modulation behavior of H-ALMBA can be insensitive to load mismatch by leveraging bias reconfiguration and the intrinsic load-insensitivity of balanced topology. Specifically, the PA's linearity and efficiency profiles can be maintained against arbitrary load mismatch through $Z_\mathrm{L}$-dependent reconfiguration of CA supply voltage ($V_\mathrm{DD,CA}$) and turning-on sequence of BA1 and BA2. Based on the proposed theory, an RF-input linear H-ALMBA is developed with GaN transistors and wideband quadrature hybrids. Over the design bandwidth from $1.7$-$2.9$ GHz, an efficiency of $56.8\%$$-$$72.9\%$ at peak power and $49.8\%$$-$$61.2\%$ at $10$-dB PBO are measured together with linear AMAM and AMPM responses. In modulated evaluation with 4G LTE signal, an EVM of $3.1\%$, ACPR of $-39$ dB, and average efficiency of up to $52\%$ are measured. Moreover, the reconfigurable H-ALMBA experimentally maintains an excellent average efficiency and linearity against arbitrary load mismatch at $2:1$ VSWR, and this mismatch-resilient operation can be achieved at any in-band frequencies. The overall measured performance favorably outperforms the state-of-the-art.

eess.SY↗

arXiv2023

Statistical Parameterized Physics-Based Machine Learning Digital Twin Models for Laser Powder Bed Fusion Process

A digital twin (DT) is a virtual representation of physical process, products and/or systems that requires a high-fidelity computational model for continuous update through the integration of sensor data and user input. In the context of laser powder bed fusion (LPBF) additive manufacturing, a digital twin of the manufacturing process can offer predictions for the produced parts, diagnostics for manufacturing defects, as well as control capabilities. This paper introduces a parameterized physics-based digital twin (PPB-DT) for the statistical predictions of LPBF metal additive manufacturing process. We accomplish this by creating a high-fidelity computational model that accurately represents the melt pool phenomena and subsequently calibrating and validating it through controlled experiments. In PPB-DT, a mechanistic reduced-order method-driven stochastic calibration process is introduced, which enables the statistical predictions of the melt pool geometries and the identification of defects such as lack-of-fusion porosity and surface roughness, specifically for diagnostic applications. Leveraging data derived from this physics-based model and experiments, we have trained a machine learning-based digital twin (PPB-ML-DT) model for predicting, monitoring, and controlling melt pool geometries. These proposed digital twin models can be employed for predictions, control, optimization, and quality assurance within the LPBF process, ultimately expediting product development and certification in LPBF-based metal additive manufacturing.

cs.LG↗

arXiv2023

Extended tensor decomposition model reduction methods: training, prediction, and design under uncertainty

This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the approximation accuracy and the reducibility (compressibility) in highly nonlinear and singular cases. The proposed XTD method can be a powerful tool for solving nonlinear space-time parametric problems. The method has been successfully applied to parametric elastic-plastic problems and real time additive manufacturing residual stress predictions with uncertainty quantification. Furthermore, a combined XTD-SCA (self-consistent clustering analysis) strategy has been presented for multi-scale material modeling, which enables real time multi-scale multi-parametric simulations. The efficiency of the method is demonstrated with comparison to finite element analysis. The proposed method enables a novel framework for fast manufacturing and material design with uncertainties.

math.NA↗