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Light Field Networks, the re-formulations of radiance fields to oriented rays, are magnitudes faster than their coordinate network counterparts, and provide higher fidelity with respect to representing 3D structures from 2D observations. They would be well suited for generic scene representation and manipulation, but suffer from one problem: they are limited to holistic and static scenes. In this paper, we propose the Dynamic Light Field Network (DyLiN) method that can handle non-rigid deformations, including topological changes. We learn a deformation field from input rays to canonical rays, and lift them into a higher dimensional space to handle discontinuities. We further introduce CoDyLiN, which augments DyLiN with controllable attribute inputs. We train both models via knowledge distillation from pretrained dynamic radiance fields. We evaluated DyLiN using both synthetic and real world datasets that include various non-rigid deformations. DyLiN qualitatively outperformed and quantitatively matched state-of-the-art methods in terms of visual fidelity, while being 25 - 71x computationally faster. We also tested CoDyLiN on attribute annotated data and it surpassed its teacher model. Project page: https://dylin2023.github.io. 

We have derived a 3-D kinetic-based discrete dynamic system (DDS) from the lattice Boltzmann equation (LBE) for incompressible flows through a Galerkin procedure. Expressed by a poor-man lattice Boltzmann equation (PMLBE), it involves five bifurcation parameters including relaxation time from the LBE, splitting factor of large and sub-grid motion scales, and wavevector components from the Fourier space. Numerical experiments have shown that the DDS can capture laminar behaviors of periodic, subharmonic, n-period, and quasi-periodic and turbulent behaviors of noisy periodic with harmonic, noisy subharmonic, noisy quasi-periodic, and broadband power spectra. In this work, we investigated the effects of bifurcation parameters on the capturing of the laminar and turbulent flows in terms of the convergence of time series and the pattern of power spectra. We have found that the 2nd order and 3rd order PMLBEs are both able to capture laminar and turbulent flow behaviors but the 2nd order DDS performs better with lower computation cost and more flow behaviors captured. With the specified ranges of the bifurcation parameters, we have identified two optimal bifurcation parameter sets for laminar and turbulent behaviors. Beyond this work, we are exploring the regime maps for a deeper understanding of the contributions of the bifurcation parameters to the capturing of laminar and turbulent behaviors. Surrogate models (to replace the PMLBE) are being developed using deep learning techniques to overcome the overwhelming computation cost for the regime maps. Meanwhile, the DDS is being employed in the large eddy simulation of turbulent pulsatile flows to provide dynamic sub-grid scale information. 

Computational fluid dynamics (CFD) and its uncertainty quantification are computationally expensive. We use Gaussian Process (GP) methods to demonstrate that machine learning can build efficient and accurate surrogate models to replace CFD simulations with significantly reduced computational cost without compromising the physical accuracy. We also demonstrate that both epistemic uncertainty (machine learning model uncertainty) and aleatory uncertainty (randomness in the inputs of CFD) can be accommodated when the machine learning model is used to reveal fluid dynamics. The demonstration is performed by applying simulation of Hagen-Poiseuille and Womersley flows that involve spatial and spatial-tempo responses, respectively. Training points are generated by using the analytical solutions with evenly discretized spatial or spatial-temporal variables. Then GP surrogate models are built using supervised machine learning regression. The error of the GP model is quantified by the estimated epistemic uncertainty. The results are compared with those from GPU-accelerated volumetric lattice Boltzmann simulations. The results indicate that surrogate models can produce accurate fluid dynamics (without CFD simulations) with quantified uncertainty when both epistemic and aleatory uncertainties exist. 

We investigate the regularity of the free boundaries in the three elastic membranes problem. We show that the two free boundaries corresponding to the coincidence regions between consecutive membranes are C1,log-hypersurfaces near a regular intersection point. We also study two types of singular intersections. The first type of singular points are locally covered by a C1,alpha-hypersurface. The second type of singular points stratify and each stratum is locally covered by a C1-manifold. 

The properties of concretes are controlled by the rate of reaction of their precursors, the chemical composition of the binding phase(s), and their structure at different scales. However, the complex and multiscale structure of the cementitious hydrates and the dissimilar rates of numerous chemical reactions make it challenging to eluci- date such linkages. In particular, reliable predictions of strength development in concretes remain unavailable. As an alternative route to physics- or chemistry-based models, machine learning (ML) offers a means to develop powerful predictive models for materials using existing data. Here, it is shown that ML models can be used to accurately predict concrete’s compressive strength at 28 days. This approach relies on the analysis of a large data set (>10,000 observations) of measured compressive strengths for industrially produced concretes, based on knowledge of their mixture proportions. It is demonstrated that these models can readily predict the 28-day compressive strength of any concrete based merely on the knowledge of the mixture proportions with an accuracy of approximately ±4.4 MPa (as captured by the root- mean-square error). By comparing the performance of select ML algorithms, the balance between accuracy, simplicity, and inter- pretability in ML approaches is discussed.