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In this paper, we present a novel flow model and compensation strategy for high-viscosity fluid deposition that yields high quality parts in the face of large transient delays and nonlinearity. Robotic high-viscosity fluid deposition is an…
A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method is a predictor-corrector strategy to define the grid…
In this study, we find the optimal control boundary (i.e., actuator velocity) that cancels the acoustic reverberations inside drop-on-demand inkjet printheads at a specific time. We formulate an optimization problem to minimize the total…
We introduce a new graph diffusion model for small molecule generation, DMol, which outperforms the state-of-the-art DiGress model in terms of validity by roughly 1.5% across all benchmarking datasets while reducing the number of diffusion…
The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate…
In this paper, we proposed a central moment discrete unified gas-kinetic scheme (DUGKS) for multiphase flows with large density ratio and high Reynolds number. Two sets of kinetic equations with central-moment-based multiple relaxation time…
Safety mechanisms for diffusion and flow models have recently been developed along two distinct paths. In robot planning, control barrier functions are employed to guide generative trajectories away from obstacles at every denoising step by…
In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of…
We present a novel monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction (FSI) problem with a thick structure. A pressure-robust optimal energy-norm estimate is obtained for the semidiscrete scheme. When…
In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D…
Microfluidic systems are now being designed with precision to execute increasingly complex tasks. However, their operation often requires numerous external control devices due to the typically linear nature of microscale flows, which has…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
Flows of particles through bottlenecks are ubiquitous in nature and industry, involving both dry granular materials and suspensions. However, practical limitations of conventional experimental setups hinder the full understanding of these…
The discovery of inorganic crystal structures with targeted properties is a significant challenge in materials science. Generative models, especially state-of-the-art diffusion models, offer the promise of modeling complex data…
We present a divergence-free and $H(div)$-conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving stationary incompressible viso-resistive magnetohydrodynamic…
This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…
A computationally accurate and efficient numerical method under a unified framework is crucial to various multi-scale scientific and engineering problems. So far, many numerical methods have encountered various challenges in efficiently…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…