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Radiofrequency ablation (RFA) is a widely used minimally invasive technique for ablating solid tumors. Achieving precise personalized treatment necessitates feedback information on in situ thermal effects induced by the RFA procedure. While computer simulation facilitates the prediction of electrical and thermal phenomena associated with RFA, its practical implementation in clinical settings is hindered by high computational demands. In this paper, we propose a physics-guided neural network model, named PhysRFANet, to enable real-time prediction of thermal effect during RFA treatment. The networks, designed for predicting temperature distribution and the corresponding ablation lesion, were trained using biophysical computational models that integrated electrostatics, bio-heat transfer, and cell necrosis, alongside magnetic resonance (MR) images of breast cancer patients. Validation of the computational model was performed through experiments on ex vivo bovine liver tissue. Our model demonstrated a 96% Dice score in predicting the lesion volume and an RMSE of 0.4854 for temperature distribution when tested with foreseen tumor images. Notably, even with unforeseen images, it achieved a 93% Dice score for the ablation lesion and an RMSE of 0.6783 for temperature distribution. All networks were capable of inferring results within 10 ms. The presented technique, applied to optimize the placement of the electrode for a specific target region, holds significant promise in enhancing the safety and efficacy of RFA treatments.

We apply the collision-based hybrid introduced in \cite{hauck} to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

Despite the recent development of deep learning-based point cloud upsampling, most MLP-based point cloud upsampling methods have limitations in that it is difficult to train the local and global structure of the point cloud at the same time. To solve this problem, we present a combined graph convolution and transformer for point cloud upsampling, denoted by PU-EdgeFormer. The proposed method constructs EdgeFormer unit that consists of graph convolution and multi-head self-attention modules. We employ graph convolution using EdgeConv, which learns the local geometry and global structure of point cloud better than existing point-to-feature method. Through in-depth experiments, we confirmed that the proposed method has better point cloud upsampling performance than the existing state-of-the-art method in both subjective and objective aspects. The code is available at https://github.com/dohoon2045/PU-EdgeFormer., Comment: Accepted to ICASSP 2023

A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and approximates the fission and scattering sources on the coarser grids. The coupling of a collided transport equation, discretized on the coarse grid, with an uncollided transport equation, discretized on the fine grid, yields an algorithm that, in most cases, is more efficient than the traditional multigroup approach. The improvement over existing techniques is demonstrated for time-dependent problems with different materials, geometries, and energy groups.

The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several reasons, the first of which is that TRT is defined on a high-dimensional phase. In order to reduce the dimensionality of the phase space, classical approaches such as the P$_N$ (spherical harmonics) or the S$_N$ (discrete ordinates) ansatz are often used in the literature. In this work, we introduce a novel approach: the hybrid discrete (H$^T_N$) approximation to the radiative thermal transfer equations. This approach acquires desirable properties of both P$_N$ and S$_N$, and indeed reduces to each of these approximations in various limits: H$^1_N$ $\equiv$ P$_N$ and H$^T_0$ $\equiv$ S$_T$. We prove that H$^T_N$ results in a system of hyperbolic equations for all $T\ge 1$ and $N\ge 0$. Another challenge in solving the TRT system is the inherent stiffness due to the large timescale separation between propagation and collisions, especially in the diffusive (i.e., highly collisional) regime. This stiffness challenge can be partially overcome via implicit time integration, although fully implicit methods may become computationally expensive due to the strong nonlinearity and system size. On the other hand, explicit time-stepping schemes that are not also asymptotic-preserving in the highly collisional limit require resolving the mean-free path between collisions, making such schemes prohibitively expensive. In this work we develop a numerical method that is based on a nodal discontinuous Galerkin discretization in space, coupled with a semi-implicit discretization in time. We conduct several numerical experiments to verify the accuracy, efficiency, and robustness of the H$^T_N$ ansatz and the numerical discretizations., Comment: 33 pages, 11 figures, 1 table