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Complex real-world optimization problems often involve both discrete decisions and nonlinear relationships between variables. Many such problems can be modeled as polynomial-objective integer programs, encompassing cases with quadratic and…
Neural networks find widespread use in scientific and technological applications, yet their implementations in conventional computers have encountered bottlenecks due to ever-expanding computational needs. Photonic neuromorphic hardware,…
Power Normalizations (PN) are very useful non-linear operators in the context of Bag-of-Words data representations as they tackle problems such as feature imbalance. In this paper, we reconsider these operators in the deep learning setup by…
Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…
Quantifying hemodynamics in the curved segments of the intracranial internal carotid artery is a core challenge in diagnosing vascular stenosis. Conventional full-field imaging, such as 4D Flow MRI, is costly and difficult to widely…
We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data…
We illustrate the use of tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, model comparison techniques) in addition to sensitivity that may be employed to determine the…
Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning…
Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed…
Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect…
The versatile physical properties of heterogeneous materials are intimately related to their complex microstructures, which can be statistically characterized and modelled using various spatial correlation functions containing key…
Convolutional Neural Networks (CNN) based image reconstruction methods have been intensely used for X-ray computed tomography (CT) reconstruction applications. Despite great success, good performance of this data-based approach critically…
Imaging inverse problems aim to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior…
Magnetic Particle Imaging (MPI) is a recent imaging modality where superparamagnetic nanoparticles are employed as tracers. The reconstruction task is to obtain the spatial particle distribution from a voltage signal induced by the…
We employ physics-informed neural networks (PINNs) to quantify the microstructure of a polycrystalline Nickel by computing the spatial variation of compliance coefficients (compressibility, stiffness and rigidity) of the material. The PINN…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
In this paper, we will introduce a novel deep model named Reconciled Polynomial Network (RPN) for deep function learning. RPN has a very general architecture and can be used to build models with various complexities, capacities, and levels…
Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…
p-spin glasses, characterized by frustrated many-body interactions beyond the conventional pairwise case (p>2), are prototypical disordered systems whose ground-state search is NP-hard and computationally prohibitive for large instances.…