Siddhant Kumar

Prakash Thakolkaran, Akshay Joshi, Yiwen Zheng et al.

We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress-strain pairs, the approach only uses realistically measurable full-field displacement and global reaction force data, thus it lies within the scope of our recent framework for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID) and we denote it as NN-EUCLID. The absence of stress labels is compensated for by leveraging a physics-motivated loss function based on the conservation of linear momentum to guide the learning process. The constitutive model is based on input-convex neural networks, which are capable of learning a function that is convex with respect to its inputs. By employing a specially designed neural network architecture, multiple physical and thermodynamic constraints for hyperelastic constitutive laws, such as material frame indifference, (poly-)convexity, and stress-free reference configuration are automatically satisfied. We demonstrate the ability of the approach to accurately learn several hidden isotropic and anisotropic hyperelastic constitutive laws - including e.g., Mooney-Rivlin, Arruda-Boyce, Ogden, and Holzapfel models - without using stress data. For anisotropic hyperelasticity, the unknown anisotropic fiber directions are automatically discovered jointly with the constitutive model. The neural network-based constitutive models show good generalization capability beyond the strain states observed during training and are readily deployable in a general finite element framework for simulating complex mechanical boundary value problems with good accuracy.

Navodini Wijethilake, Marina Ivory, Oscar MacCormac et al.

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).

Yaqi Guo, Fabian Braun, Bastiaan Ketelaar et al.

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.

Benjamin Alheit, Mathias Peirlinck, Siddhant Kumar

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.

Yiwen Zheng, Prakash Thakolkaran, Agni K. Biswal et al.

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.

Prakash Thakolkaran, Yaqi Guo, Shivam Saini et al.

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.

Rogier P. Krijnen, Akshay Joshi, Siddhant Kumar et al.

Fully capturing this behavior in traditional homogenized tissue testing requires the excitation of multiple deformation modes, i.e. combined triaxial shear tests and biaxial stretch tests. Inherently, such multimodal experimental protocols necessitate multiple tissue samples and extensive sample manipulations. Intrinsic inter-sample variability and manipulation-induced tissue damage might have an adverse effect on the inversely identified tissue behavior. In this work, we aim to overcome this gap by focusing our attention to the use of heterogeneous deformation profiles in a parameter estimation problem. More specifically, we adapt EUCLID, an unsupervised method for the automated discovery of constitutive models, towards the purpose of parameter identification for highly nonlinear, orthotropic constitutive models using a Bayesian inference approach and three-dimensional continuum elements. We showcase its strength to quantitatively infer, with varying noise levels, the material model parameters of synthetic myocardial tissue slabs from a single heterogeneous biaxial stretch test. This method shows good agreement with the ground-truth simulations and with corresponding credibility intervals. Our work highlights the potential for characterizing highly nonlinear and orthotropic material models from a single biaxial stretch test with uncertainty quantification.

Li Zheng, Siddhant Kumar, Dennis M. Kochmann

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 a novel algebraic language representation, encoding 3D geometries as mathematical sentences. This compact, unified parameterization spans diverse topologies while enabling direct application of transformers to structural design. DiffuMeta leverages diffusion models to generate novel 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.