arXiv subjects

Siddhant Kumar

Publications and source records attributed to Siddhant Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Data-efficient continuous conditional denoising diffusion model for microstructure generation

Traditional computational models, such as cellular automata and phase-field methods, are effective for simulating microstructural evolution but often face computational bottlenecks, limiting their application in high-throughput and on-demand process optimization. Generative machine learning approaches, such as denoising diffusion models, have emerged as powerful tools for surrogate modeling of process-structure maps, specifically producing representative microstructures conditioned on process parameters. However, they often require large amounts of data for training, particularly when process conditions are continuous rather than discrete categorical variables. To address this, we present a continuous conditional denoising diffusion model for generating microstructures conditioned on processing parameters. Trained on a compact dataset of process-microstructure pairs, this framework first adds noise to microstructure images and then trains a neural network to progressively remove the noise, learning the underlying statistical patterns of the microstructure. To address data inefficiencies associated with continuously valued process conditions, we propose a vicinal-loss training strategy that associates process conditions in data-sparse regions with nearby conditions in the dataset. Combined with classifier-free guidance and denoising diffusion implicit sampling, this approach enables data-efficient continuous conditional generation of microstructures compared to classical denoising diffusion models. The model successfully generates representative microstructures for low-carbon steel conditioned on manganese composition, matching key physical features such as phase and grain morphology, grain size distribution, phase fraction, and interfacial area distribution. More generally, this approach opens avenues for efficient process design and optimization of materials and their microstructures.

cs.CE↗

arXiv2026

CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data

Constitutive artificial neural networks (CANNs) provide interpretable material model discovery, but have so far been used in stress-supervised settings based on apparent stress-strain data from homogeneous tests. Because each test samples only a narrow loading path and provides homogenized rather than local stress information, robust discovery typically requires multiple loading modes to constrain the multidimensional response. This is challenging for soft biological tissues, where repeated testing, damage, and sample variability limit reliable information from a single specimen. Here, we combine CANNs with the stress-unsupervised full-field discovery framework EUCLID to identify sparse hyperelastic laws directly from displacement fields and reaction forces in one heterogeneity-inducing loading case. CANN-EUCLID minimizes equilibrium imbalance with sparsity-promoting regularization selecting compact active terms, without local stress measurements or a prescribed law. We evaluate the approach on isotropic and anisotropic benchmarks with prescribed ground-truth laws. When the ground truth is representable by the chosen CANN basis, our method recovers the correct terms with near-exact accuracy, including exponential terms with embedded parameters. When it is not contained in the basis, the method retains shared terms and approximates missing contributions using available basis functions. Generalization depends strongly on sampled deformation states: exponential strain-stiffening terms can be recovered accurately when sufficiently probed, but can produce large extrapolation errors when the stiffening regime lies outside the sampled domain. Forward FE validation simulations show that the discovered behavior accurately replicates the ground truth. These results establish stress-unsupervised CANN discovery as a promising framework for interpretable full-field constitutive model identification.

cs.CE↗

arXiv2026

Local learning for stable backpropagation-free neural network training towards physical learning

While backpropagation and automatic differentiation have driven deep learning's success, the physical limits of chip manufacturing and rising environmental costs of deep learning motivate alternative learning paradigms such as physical neural networks. However, most existing physical neural networks still rely on digital computing for training, largely because backpropagation and automatic differentiation are difficult to realize in physical systems. We introduce FFzero, a forward-only learning framework enabling stable neural network training without backpropagation or automatic differentiation. FFzero combines layer-wise local learning, prototype-based representations, and directional-derivative-based optimization through forward evaluations only. We show that local learning is effective under forward-only optimization, where backpropagation fails. FFzero generalizes to multilayer perceptron and convolutional neural networks across classification and regression. Using a simulated photonic neural network as an example, we demonstrate that FFzero provides a viable path toward backpropagation-free in-situ physical learning.

cs.LG↗

arXiv2025

Longitudinal Vestibular Schwannoma Dataset with Consensus-based Human-in-the-loop Annotations

Accurate segmentation of vestibular schwannoma (VS) on Magnetic Resonance Imaging (MRI) is essential for patient management but often requires time-intensive manual annotations by experts. While recent advances in deep learning (DL) have facilitated automated segmentation, challenges remain in achieving robust performance across diverse datasets and complex clinical cases. We present an annotated dataset stemming from a bootstrapped DL-based framework for iterative segmentation and quality refinement of VS in MRI. We combine data from multiple centres and rely on expert consensus for trustworthiness of the annotations. We show that our approach enables effective and resource-efficient generalisation of automated segmentation models to a target data distribution. The framework achieved a significant improvement in segmentation accuracy with a Dice Similarity Coefficient (DSC) increase from 0.9125 to 0.9670 on our target internal validation dataset, while maintaining stable performance on representative external datasets. Expert evaluation on 143 scans further highlighted areas for model refinement, revealing nuanced cases where segmentation required expert intervention. The proposed approach is estimated to enhance efficiency by approximately 37.4% compared to the conventional manual annotation process. Overall, our human-in-the-loop model training approach achieved high segmentation accuracy, highlighting its potential as a clinically adaptable and generalisable strategy for automated VS segmentation in diverse clinical settings. The dataset includes 190 patients, with tumour annotations available for 534 longitudinal contrast-enhanced T1-weighted (T1CE) scans from 184 patients, and non-annotated T2-weighted scans from 6 patients. This dataset is publicly accessible on The Cancer Imaging Archive (TCIA) (https://doi.org/10.7937/bq0z-xa62).

cs.CV↗

arXiv2025

Discovery of Hyperelastic Constitutive Laws from Experimental Data with EUCLID

We assess the performance of EUCLID, Efficient Unsupervised Constitutive Law Identification and Discovery, a recently proposed framework for automated discovery of constitutive laws, on experimental data. Mechanical tests are performed on natural rubber specimens spanning simple to complex geometries, from which we collect both global, force elongation, and local, full-field displacement, measurements. Using these data, we obtain constitutive laws via two routes, the conventional identification of unknown parameters in a priori selected material models, and EUCLID, which automates model selection and parameter identification within a unified model-discovery pipeline. We compare the two methodologies using global versus local data, analyze predictive accuracy, and examine generalization to unseen geometries. Moreover, we quantify the experimental noise, investigate the coverage of the material state space achieved by each approach and discuss the relative performance of different datasets and different a priori chosen models versus EUCLID.

physics.comp-ph↗

arXiv2025

Unsupervised full-field Bayesian inference of orthotropic hyperelasticity from a single biaxial test: a myocardial case study

Cardiac muscle tissue exhibits highly non-linear hyperelastic and orthotropic material behavior during passive deformation. Traditional constitutive identification protocols therefore combine multiple loading modes and typically require multiple specimens and substantial handling. In soft living tissues, such protocols are challenged by inter- and intra-sample variability and by manipulation-induced alterations of mechanical response, which can bias inverse calibration. In this work we exploit spatially heterogeneous full-field kinematics as an information-rich alternative to multimodal testing. We recast EUCLID, an unsupervised method for the automated discovery of constitutive models, towards Bayesian parameter inference for highly nonlinear, orthotropic constitutive models. Using synthetic myocardial tissue slabs, we demonstrate that a single heterogeneous biaxial experiment, combined with sparse reaction-force measurements, enables robust recovery of Holzapfel-Ogden parameters with quantified uncertainty, across multiple noise levels. The inferred responses agree closely with ground-truth simulations and yield credible intervals that reflect the impact of measurement noise on orthotropic material model inference. Our work supports single-shot, uncertainty-aware characterization of nonlinear orthotropic material models from a single biaxial test, reducing sample demand and experimental manipulation.

q-bio.TO↗

arXiv2025

COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates

Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex material behavior in solid mechanics. However, their practical adoption in large-scale FE simulations remains limited due to significant computational costs, especially in repeatedly evaluating stress and stiffness. NCMs thus represent an extreme case: their large computational graphs make stress and stiffness evaluations prohibitively expensive, restricting their use to small-scale problems. In this work, we introduce COMMET, an open-source FE framework whose architecture has been redesigned from the ground up to accelerate high-cost constitutive updates. Our framework features a novel assembly algorithm that supports batched and vectorized constitutive evaluations, compute-graph-optimized derivatives that replace automatic differentiation, and distributed-memory parallelism via MPI. These advances dramatically reduce runtime, with speed-ups exceeding three orders of magnitude relative to traditional non-vectorized automatic differentiation-based implementations. While we demonstrate these gains primarily for NCMs, the same principles apply broadly wherever for-loop based assembly or constitutive updates limit performance, establishing a new standard for large-scale, high-fidelity simulations in computational mechanics.

cs.CE↗

arXiv2025

Hetero-EUCLID: Interpretable model discovery for heterogeneous hyperelastic materials using stress-unsupervised learning

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) framework to efficiently solve the heterogenized formulation through parsimonious model selection using sparsity-promoting priors and Monte Carlo Markov Chain sampling. We utilize experimentally observable 3D surface displacement and boundary-averaged force data generated from Finite Element simulations of non-equi-biaxial tension tests on heterogeneous specimens. The framework broadly consists of two steps -- residual force-based segmentation, and constitutive parameter identification. We validate and demonstrate the ability of the proposed framework to segment the domain, and characterize the constituent materials on various types of thin square heterogeneous domains. We validate of the framework's ability to segment and characterize materials with various levels of displacement noises and non-native mesh discretizations, i.e, using different meshes for the forward FE simulations and the inverse EUCLID problem. This demonstrates Hetero-EUCLID framework's applicability in Digital Image/Volume Correlation-based experimental scenarios. Furthermore, the proposed framework performs successful segmentation and material characterizations based on data from a single experiment, thereby making it viable for rapid, interpretable model discovery in domains such as aerospace and defense composites and for characterization of selective tissue stiffening in medical conditions such as fibroatheroma, atherosclerosis, or cancer.

cs.CE↗

arXiv2025

Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers

Generative machine learning models have revolutionized material discovery by capturing complex structure-property relationships, yet extending these approaches to the inverse design of three-dimensional metamaterials remains limited by computational complexity and underexplored design spaces due to the lack of expressive representations. Here we present DiffuMeta, a generative framework integrating diffusion transformers with an algebraic language representation, encoding three-dimensional geometries as mathematical sentences. This compact, unified parameterization spans diverse topologies, enabling the direct application of transformers to structural design. DiffuMeta leverages diffusion models to generate new shell structures with precisely targeted stress-strain responses under large deformations, accounting for buckling and contact while addressing the inherent one-to-many mapping by producing diverse solutions. Uniquely, our approach enables simultaneous control over multiple mechanical objectives, including linear and nonlinear responses beyond training domains. Experimental validation of fabricated structures further confirms the efficacy of our approach for accelerated design of metamaterials and structures with tailored properties.

cs.CE↗

arXiv2025

Piezoelectric truss metamaterials: data-driven design and additive manufacturing

In the development of active animate materials, electromechanical coupling is highly attractive to realize mechanoresponsive functionality. Piezoelectricity is the most utilized electromechanical phenomenon due to the wide availability of materials that display precise and reliable coupling. However, the inherent directionality of these materials is constrained by the symmetry of their crystal structure, which limits the choice of available properties in natural piezoelectric materials. A solution to alleviate this limitation could be to leverage geometry or architecture at the mesoscale. Here, we present an integrated framework to design and 3D-print piezoelectric truss metamaterials with customizable anisotropic responses. To explore the vast design space of truss metamaterials, we employ generative machine learning to optimize the topology and geometry of truss lattices and achieve target piezoelectricity. Then, we develop an in-gel-3D printing method to fabricate polymer-ceramic piezoelectric truss metamaterial structures using a composite slurry of photo-curable resin and lead-free piezoelectric particles. The ML framework discovers designs exhibiting unconventional behaviors, including auxetic, unidirectional, and omnidirectional piezoelectricity, while the additive manufacturing technique ensures shaping freedom and precision in fabricating these metamaterials at small scales. Our results show an improvement of over 48% in the specific hydrostatic piezoelectric coefficient in optimized metamaterials over bulk lead zirconate titanate (PZT). We successfully achieved metamaterials with higher transverse piezoelectric coupling coefficient than its longitudinal coefficient, which is a phenomenon that is rare in bulk materials. Our approach enables customizable piezoelectric responses and paves the way towards the development of a new generation of electro-active animate materials.

physics.app-ph↗

arXiv2025

Toward Sustainable Polymer Design: A Molecular Dynamics-Informed Machine Learning Approach for Vitrimers

Vitrimer is an emerging class of sustainable polymers with self-healing capabilities enabled by dynamic covalent adaptive networks. However, their limited molecular diversity constrains their property space and potential applications. Recent development in machine learning (ML) techniques accelerates polymer design by predicting properties and virtually screening candidates, yet the scarcity of available experimental vitrimer data poses challenges in training ML models. To address this, we leverage molecular dynamics (MD) data generated by our previous work to train and benchmark seven ML models covering six feature representations for glass transition temperature (Tg) prediction. By averaging predicted Tg from different models, the model ensemble approach outperforms individual models, allowing for accurate and efficient property prediction on unlabeled datasets. Two novel vitrimers are identified and synthesized, exhibiting experimentally validated higher Tg than existing bifunctional transesterification vitrimers, along with demonstrated healability. This work explores the possibility of using MD data to train ML models in the absence of sufficient experimental data, enabling the discovery of novel, synthesizable polymer chemistries with superior properties. The integrated MD-ML approach offers polymer chemists an efficient tool for designing polymers tailored to diverse applications.

cond-mat.mtrl-sci↗

arXiv2025

Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold representation, decomposing the model into compositions of trainable univariate spline-based activation functions for rich expressivity. We introduce trainable monotonic input-convex splines within the KAN architecture, ensuring physically admissible polyconvex models for isotropic compressible hyperelasticity. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through a monotonic input-convex symbolic regression technique. Through unsupervised training on full-field strain data and limited global force measurements, ICKANs accurately capture nonlinear stress-strain behavior across diverse strain states. Finite element simulations of unseen geometries with trained ICKAN hyperelastic constitutive models confirm the framework's robustness and generalization capability.

cs.LG↗

arXiv2025

A topology optimisation framework to design test specimens for one-shot identification or discovery of material models

The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry tests towards a few, or even one single test with complicated geometry. The feasibility of such a "one-shot" calibration or discovery heavily relies upon the richness of the measured displacement data, i.e., their ability to probe the space of the state variables and the stress space (whereby the stresses depend on the constitutive law being sought) to an extent sufficient for an accurate and robust calibration or discovery process. The richness of the displacement data is in turn directly governed by the specimen geometry. In this paper, we propose a density-based topology optimisation framework to optimally design the geometry of the target specimen for calibration of an anisotropic elastic material model. To this end, we perform automatic, high-resolution specimen design by maximising the robustness of the solution of the inverse problem, i.e., the identified material parameters, given noisy displacement measurements from digital image correlation. We discuss the choice of the cost function and the design of the topology optimisation framework, and we analyse a range of optimised topologies generated for the identification of isotropic and anisotropic elastic responses.

cs.CE↗

arXiv2024

Deep learning reveals key predictors of thermal conductivity in covalent organic frameworks

The thermal conductivity of covalent organic frameworks (COFs), an emerging class of nanoporous polymeric materials, is crucial for many applications, yet the link between their structure and thermal properties remains poorly understood. Analysis of a dataset containing over 2,400 COFs reveals that conventional features such as density, pore size, void fraction, and surface area do not reliably predict thermal conductivity. To address this, an attention-based machine learning model was trained, accurately predicting thermal conductivities even for structures outside the training set. The attention mechanism was then utilized to investigate the model's success. The analysis identified dangling molecular branches as a key predictor of thermal conductivity, leading us to define the dangling mass ratio (DMR), a descriptor that quantifies the fraction of atomic mass in dangling branches relative to the total COF mass. Feature importance assessments on regression models confirm the significance of DMR in predicting thermal conductivity. These findings indicate that COFs with dangling functional groups exhibit lower thermal transfer capabilities. Molecular dynamics simulations support this observation, revealing significant mismatches in the vibrational density of states due to the presence of dangling branches.

cs.CE↗

arXiv2024

HyperCAN: Hypernetwork-Driven Deep Parameterized Constitutive Models for Metamaterials

We introduce HyperCAN, a machine learning framework that utilizes hypernetworks to construct adaptable constitutive artificial neural networks for a wide range of beam-based metamaterials exhibiting diverse mechanical behavior under finite deformations. HyperCAN integrates an input convex network that models the nonlinear stress-strain map of a truss lattice, while ensuring adherence to fundamental mechanics principles, along with a hypernetwork that dynamically adjusts the parameters of the convex network as a function of the lattice topology and geometry. This unified framework demonstrates robust generalization in predicting the mechanical behavior of previously unseen metamaterial designs and loading scenarios well beyond the training domain. We show how HyperCAN can be integrated into multiscale simulations to accurately capture the highly nonlinear responses of large-scale truss metamaterials, closely matching fully resolved simulations while significantly reducing computational costs. This offers new efficient opportunities for the multiscale design and optimization of truss metamaterials.

cs.CE↗

arXiv2023

Experiment-informed finite-strain inverse design of spinodal metamaterials

Spinodal metamaterials, with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance. While their elastic mechanical properties have been systematically determined, their large-deformation, nonlinear responses have been challenging to predict and design, in part due to limited data sets and the need for complex nonlinear simulations. This work presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in large-deformation scenarios where computational modeling is restrictive and experimental data is sparse. By utilizing large-deformation experimental data directly, this approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. The framework sheds light on instability-induced pattern formation in spinodal metamaterials -- observed experimentally and in selected nonlinear simulations -- leveraging physics-based inductive biases in the form of nonconvex energetic potentials. Altogether, this combined ML, experimental, and computational effort provides a route for efficient and accurate design of complex spinodal metamaterials for large-deformation scenarios where energy absorption and prediction of nonlinear failure mechanisms is essential.

cs.CE↗

arXiv2023

A discontinuous Galerkin / cohesive zone model approach for the computational modeling of fracture in geometrically exact slender beams

Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture plays a critical role. In this paper, we introduce a novel computational approach for modeling fracture in slender beams subjected to large deformations. We adopt a state-of-the-art geometrically exact Kirchhoff beam formulation to describe the finite deformations of beams in three-dimensions. We develop a discontinuous Galerkin finite element discretization of the beam governing equations, incorporating discontinuities in the position and tangent degrees of freedom at the inter-element boundaries of the finite elements. Before fracture initiation, we enforce compatibility of nodal positions and tangents weakly, via the exchange of variationally-consistent forces and moments at the interfaces between adjacent elements. At the onset of fracture, these forces and moments transition to cohesive laws modeling interface failure. We conduct a series of numerical tests to verify our computational framework against a set of benchmarks and we demonstrate its ability to capture the tensile and bending fracture modes in beams exhibiting large deformations. Finally, we present the validation of our framework against fracture experiments of dry spaghetti rods subjected to sudden relaxation of curvature.

cs.CE↗

arXiv2023

AI-guided inverse design and discovery of recyclable vitrimeric polymers

Vitrimer is a new, exciting class of sustainable polymers with the ability to heal due to their dynamic covalent adaptive network that can go through associative rearrangement reactions. However, a limited choice of constituent molecules restricts their property space, prohibiting full realization of their potential applications. To overcome this challenge, we couple molecular dynamics (MD) simulations and a novel graph variational autoencoder (VAE) machine learning model for inverse design of vitrimer chemistries with desired glass transition temperature (Tg) and synthesize a novel vitrimer polymer. We build the first vitrimer dataset of one million chemistries and calculate Tg on 8,424 of them by high-throughput MD simulations calibrated by a Gaussian process model. The proposed novel VAE employs dual graph encoders and a latent dimension overlapping scheme which allows for individual representation of multi-component vitrimers. By constructing a continuous latent space containing necessary information of vitrimers, we demonstrate high accuracy and efficiency of our framework in discovering novel vitrimers with desirable Tg beyond the training regime. To validate the effectiveness of our framework in experiments, we generate novel vitrimer chemistries with a target Tg = 323 K. By incorporating chemical intuition, we synthesize a vitrimer with Tg of 311-317 K, and experimentally demonstrate healability and flowability. The proposed framework offers an exciting tool for polymer chemists to design and synthesize novel, sustainable vitrimer polymers for a facet of applications.

cond-mat.mtrl-sci↗