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The process of screening molecules for desirable properties is a key step in several applications, ranging from drug discovery to material design. During the process of drug discovery specifically, protein-ligand docking, or chemical…
Hierarchical matrices provide a powerful representation for significantly reducing the computational complexity associated with dense kernel matrices. For general kernel functions, interpolation-based methods are widely used for the…
Due to the over-smoothing issue, most existing graph neural networks can only capture limited dependencies with their inherently finite aggregation layers. To overcome this limitation, we propose a new kind of graph convolution, called…
Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated…
We develop and analyze a stochastic genetic interacting particle method (SGIP) for reaction-diffusion-advection (RDA) equations. The SGIP method employs operator splitting to approximate the advection-diffusion and reaction processes,…
We investigate the rate of convergence of linear sampling numbers of the embedding $H^{\alpha,\beta} (\mathbb{T}^d) \hookrightarrow H^\gamma (\mathbb{T}^d)$. Here $\alpha$ governs the mixed smoothness and $\beta$ the isotropic smoothness in…
We present the sliding basis computational framework to automatically synthesize heterogeneous (graded or discrete) material fields for parts designed using constrained optimization. Our framework uses the fact that any spatially varying…
Temporal Interaction Graphs (TIGs) are widely employed to model intricate real-world systems such as financial systems and social networks. To capture the dynamism and interdependencies of nodes, existing TIG embedding models need to…
Graph representation learning seeks to transform complex, high-dimensional graph structures into compact vector spaces that preserve both topology and semantics. Among the various strategies, subgraph-based methods provide an interpretable…
Photopolymerization enables the production of micro-optical elements, such as diffractive optical elements or GRIN optics. This process utilizes targeted spatial modulation of the refractive index, which is achieved through additive…
Topology optimization is one of the engineering tools for finding efficient design. For the material interpolation scheme, it is usual to employ the SIMP (Solid Isotropic Material with Penalization) or the homogenization based interpolation…
Pose graph optimization is a non-convex optimization problem encountered in many areas of robotics perception. Its convergence to an accurate solution is conditioned by two factors: the non-linearity of the cost function in use and the…
Graph generation generally aims to create new graphs that closely align with a specific graph distribution. Existing works often implicitly capture this distribution through the optimization of generators, potentially overlooking the…
Chiplet-based systems, integrating various silicon dies manufactured at different integrated circuit technology nodes on a carrier interposer, have garnered significant attention in recent years due to their cost-effectiveness and…
Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data…
Graph Neural Networks (GNNs) with numerical node features and graph structure as inputs have demonstrated superior performance on various supervised learning tasks with graph data. However the numerical node features utilized by GNNs are…
Following the success of convolution on non-Euclidean space, the corresponding pooling approaches have also been validated on various tasks regarding graphs. However, because of the fixed compression quota and stepwise pooling design, these…
Retrieval-Augmented Generation (RAG) enhances large language models (LLMs) by integrating external knowledge retrieval but faces challenges on edge devices due to high storage, energy, and latency demands. Computing-in-Memory (CIM) offers a…
Genome assembly is a prominent problem studied in bioinformatics, which computes the source string using a set of its overlapping substrings. Classically, genome assembly uses assembly graphs built using this set of substrings to compute…
Graph embedding approaches attempt to project graphs into geometric entities, i.e, manifolds. The idea is that the geometric properties of the projected manifolds are helpful in the inference of graph properties. However, if the choice of…