Related papers: Constitutive Manifold Neural Networks
In these pedagogic notes I review the statistical mechanics approach to neural networks, focusing on the paradigmatic example of the perceptron architecture with binary an continuous weights, in the classification setting. I will review the…
Recent advances in optimization methods used for training convolutional neural networks (CNNs) with kernels, which are normalized according to particular constraints, have shown remarkable success. This work introduces an approach for…
Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory…
Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…
Neural Processes (NPs) are meta-learning models that learn to map sets of observations to approximations of the corresponding posterior predictive distributions. By accommodating variable-sized, unstructured collections of observations and…
Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to…
In practical structural design and solid mechanics simulations, material properties inherently exhibit random variations within bounded intervals. However, evaluating mechanical responses under continuous material uncertainty remains a…
Since their introduction, Transformer architectures have dominated Natural Language Processing (NLP). However, recent research has highlighted an inherent anisotropy phenomenon in these models, presenting a significant challenge to their…
Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…
Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct…
Stochastic configuration networks (SCNs), as a class of randomized learner models, are featured by its way of random parameters assignment in the light of a supervisory mechanism, resulting in the universal approximation property at…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
Carbon fiber and graphene-based nanostructures such as carbon nanotubes (CNTs) and defective structures have extraordinary potential as strong and lightweight materials. A longstanding bottleneck has been lack of understanding and…
Human tissues are highly organized structures with collagen fiber arrangements varying from point to point. Anisotropy of the tissue arises from the natural orientation of the fibers, resulting in location-dependent anisotropy.…
Deep neural networks have become the main work horse for many tasks involving learning from data in a variety of applications in Science and Engineering. Traditionally, the input to these networks lie in a vector space and the operations…
Real-time reconstruction of conditional quantum states from continuous measurement records is a fundamental requirement for quantum feedback control, yet standard stochastic master equation (SME) solvers require exact model specification,…
We study a deep linear network endowed with a structure. It takes the form of a matrix $X$ obtained by multiplying $K$ matrices (called factors and corresponding to the action of the layers). The action of each layer (i.e. a factor) is…
In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…
Germanium manganese compounds exhibit a variety of stable and metastable phases with different stoichiometry. These materials entail interesting electronic, magnetic and thermal properties both in their bulk form and as heterostructures.…
In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using…