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This thesis is about the study of complex systems through simple models. Our work evidences the relevance of this kind of modeling in science, which provides us with a better understanding of nature at minimum cost. The fundamentals tools…
Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasi-continuum method links atomistic and…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
While successful for various computer vision tasks, deep neural networks have shown to be vulnerable to texture style shifts and small perturbations to which humans are robust. In this work, we show that the robustness of neural networks…
Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of…
Development of algorithms and growth of computational resources in the past decades have enabled simulations of sediment transport processes with unprecedented fidelities. The Computational Fluid Dynamics--Discrete Element Method (CFD--DEM)…
When modeling microstructures, the computational resource requirements increase rapidly as the simulation domain becomes larger. As a result, simulating a small representative fraction under periodic boundary conditions is often a necessary…
Composite of two kinds of grains is modeled in two-dimension and the elasticity is calculated using molecular dynamics method implementing Gear predictor-corrector of fifth order. It has been observed that same composite concentration can…
Convolutional Neural Networks have revolutionized vision applications. There are image domains and representations, however, that cannot be handled by standard CNNs (e.g., spherical images, superpixels). Such data are usually processed…
Granular materials of different sizes are present on the surface of several atmosphere-less Solar System bodies. The phenomena related to granular materials have been studied in the framework of the discipline called Granular Physics; that…
Acquiring food items with a fork poses an immense challenge to a robot-assisted feeding system, due to the wide range of material properties and visual appearances present across food groups. Deformable foods necessitate different skewering…
Determining the different conformational states of a protein and the transition paths between them is key to fully understanding the relationship between biomolecular structure and function. This can be accomplished by sampling protein…
Perceptual learning enables humans to recognize and represent stimuli invariant to various transformations and build a consistent representation of the self and physical world. Such representations preserve the invariant physical relations…
Optical imaging through complex media, such as biological tissues or fog, is challenging due to light scattering. In the multiple scattering regime, wavefront shaping provides an effective method to retrieve information; it relies on…
The elastic properties of materials derive from their electronic and atomic nature. However, simulating bulk materials fully at these scales is not feasible, so that typically homogenized continuum descriptions are used instead. A seamless…
Granular media such as sand and sugar are ubiquitous in nature and industry but are less well understood than fluids or solids. We consider the behavior of rapid granular flows where the transfer of momenta by collisions dominates. The…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
Graph neural networks (GNN) are a promising tool to predict magnetic properties of large multi-grain structures, which can speed up the search for rare-earth free permanent magnets. In this paper, we use our magnetic simulation data to…
Grain boundaries dramatically affect the properties of polycrystalline materials because of differences in atomic configuration. To fully understand the relationship between grain boundaries and materials properties, systematic studies of…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…