The kidney paired donation (KPD) program provides an innovative solution to overcome incompatibility challenges in kidney transplants by matching incompatible donor-patient pairs and facilitating kidney exchanges. To address unequal access to transplant opportunities, there are two widely used fairness criteria: group fairness and individual fairness. However, these criteria do not consider protected patient features, which refer to characteristics legally or ethically recognized as needing protection from discrimination, such as race and gender. Motivated by the calibration principle in machine learning, we introduce a new fairness criterion: the matching outcome should be conditionally independent of the protected feature, given the sensitization level. We integrate this fairness criterion as a constraint within the KPD optimization framework and propose a computationally efficient solution. Theoretically, we analyze the associated price of fairness using random graph models. Empirically, we compare our fairness criterion with group fairness and individual fairness through both simulations and a real-data example.

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dimensional dynamical systems. Key approaches discussed include graph neural networks, transformer models with spatial attention mechanisms, interpolation-integrated ML methods, and meshless techniques such as physics-informed neural networks. These methodologies have proven effective across diverse fields, including fluid dynamics and environmental simulations. This review is intended as a guidebook for computational scientists seeking to apply ML approaches to unstructured grid data in their domains, as well as for ML researchers looking to address challenges in computational physics. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques and, conversely, how insights from computational physics can inform ML development. To support benchmarking, this review also provides a summary of open-access datasets of unstructured grid data in computational physics. Finally, emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed to inspire future advancements in this evolving field.

While recent advancements have shown remarkable progress in general 3D shape generation models, the challenge of leveraging these approaches to automatically generate wearable 3D assets remains unexplored. To this end, we present BAG, a Body-aligned Asset Generation method to output 3D wearable asset that can be automatically dressed on given 3D human bodies. This is achived by controlling the 3D generation process using human body shape and pose information. Specifically, we first build a general single-image to consistent multiview image diffusion model, and train it on the large Objaverse dataset to achieve diversity and generalizability. Then we train a Controlnet to guide the multiview generator to produce body-aligned multiview images. The control signal utilizes the multiview 2D projections of the target human body, where pixel values represent the XYZ coordinates of the body surface in a canonical space. The body-conditioned multiview diffusion generates body-aligned multiview images, which are then fed into a native 3D diffusion model to produce the 3D shape of the asset. Finally, by recovering the similarity transformation using multiview silhouette supervision and addressing asset-body penetration with physics simulators, the 3D asset can be accurately fitted onto the target human body. Experimental results demonstrate significant advantages over existing methods in terms of image prompt-following capability, shape diversity, and shape quality. Our project page is available at https://bag-3d.github.io/.

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Amp\`ere PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.

Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical learning framework that outputs unified NN controllers capable of tasks with significantly improved complexity and diversity. To systematically improve training robustness and efficiency, we investigated a suite of improvements over the baseline approach, including periodic activation functions, and tailored loss functions. In addition, we find our adoption of batching and an Adam optimizer effective in training complex locomotion tasks. We evaluate our framework on differentiable mass-spring and material point method (MPM) simulations, with challenging locomotion tasks and multiple robot designs. Experiments show that our learning framework, based on differentiable physics, delivers better results than reinforcement learning and converges much faster. We demonstrate that users can interactively control soft robot locomotion and switch among multiple goals with specified velocity, height, and direction instructions using a unified NN controller trained in our system. Code is available at https://github.com/erizmr/Complex-locomotion-skill-learning-via-differentiable-physics.

As one of the cleanest and most sustainable sources of renewable energy, wind energy has been undergoing rapid and unabated expansion worldwide. As the capacity of wind turbine farms increases, through the potentially closer clustering of increasing numbers of larger turbines to most efficiently exploit the available wind energy resource, it is inevitable that downstream turbines will at some times be operating within the full or partial wakes of upstream turbines. This can lead to reduced power generation as well as increased structural loads. Consequently, wind turbine wake modelling has been widely considered as one of the most crucial aspects of the optimal design and operational control of wind farms, see [1] and the references therein. Wake models across different levels of fidelity have been thoroughly studied by researchers over the years. Analytical models including the Jensen model [2], the Larsen model [3] and the Gaussian wake model [4] are commonly implemented in industrial standard software such as FLORIS [5], thanks to their very rapid execution speed, however their accuracy is consequently limited. In comparison, higher fidelity models based on computational fluid dynamics (CFD) simulations, such as Reynolds-Averaged Navier-Stokes (RANS) or Large Eddy Simulation (LES), can provide more accurate flow field predictions but at significantly higher computational cost and execution time, hampering their value for rapid resource assessment, and as part of iterative design optimisation and control tools. For instance, the computing time required by RANS modelling for the simulation of a wind farm tends to be in the order of several CPU hours, whereas LES simulations could take days of distributed computation on hundreds of processors [6].

Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the finite element method. By decomposing the error estimates into contributions from individual elements, it is possible to formulate adaptation methods, which modify the mesh with the objective of minimising the resulting QoI error. However, the standard error estimate formulation involves the true adjoint solution, which is unknown in practice. As such, it is common practice to approximate it with an 'enriched' approximation (e.g. in a higher order space or on a refined mesh). Doing so generally results in a significant increase in computational cost, which can be a bottleneck compromising the competitiveness of (goal-oriented) adaptive simulations. The central idea of this paper is to develop a "data-driven" goal-oriented mesh adaptation approach through the selective replacement of the expensive error estimation step with an appropriately configured and trained neural network. In doing so, the error estimator may be obtained without even constructing the enriched spaces. An element-by-element construction is employed here, whereby local values of various parameters related to the mesh geometry and underlying problem physics are taken as inputs, and the corresponding contribution to the error estimator is taken as output. We demonstrate that this approach is able to obtain the same accuracy with a reduced computational cost, for adaptive mesh test cases related to flow around tidal turbines, which interact via their downstream wakes, and where the overall power output of the farm is taken as the QoI. Moreover, we demonstrate that the element-by-element approach implies reasonably low training costs.

Photo collage aims to automatically arrange multiple photos on a given canvas with high aesthetic quality. Existing methods are based mainly on handcrafted feature optimization, which cannot adequately capture high-level human aesthetic senses. Deep learning provides a promising way, but owing to the complexity of collage and lack of training data, a solution has yet to be found. In this paper, we propose a novel pipeline for automatic generation of aspect ratio specified collage and the reinforcement learning technique is introduced in collage for the first time. Inspired by manual collages, we model the collage generation as sequential decision process to adjust spatial positions, orientation angles, placement order and the global layout. To instruct the agent to improve both the overall layout and local details, the reward function is specially designed for collage, considering subjective and objective factors. To overcome the lack of training data, we pretrain our deep aesthetic network on a large scale image aesthetic dataset (CPC) for general aesthetic feature extraction and propose an attention fusion module for structural collage feature representation. We test our model against competing methods on two movie datasets and our results outperform others in aesthetic quality evaluation. Further user study is also conducted to demonstrate the effectiveness.

As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants for scalable projection-free optimization. We first propose 1-SFW, the first projection-free method that requires only one sample per iteration to update the optimization variable and yet achieves the best known complexity bounds for convex, non-convex, and monotone DR-submodular settings. Then we move forward to the distributed setting, and develop Quantized Frank-Wolfe (QFW), a general communication-efficient distributed FW framework for both convex and non-convex objective functions. We study the performance of QFW in two widely recognized settings: 1) stochastic optimization and 2) finite-sum optimization. Finally, we propose Black-Box Continuous Greedy, a derivative-free and projection-free algorithm, that maximizes a monotone continuous DR-submodular function over a bounded convex body in Euclidean space.

In this paper, we propose three online algorithms for submodular maximization. The first one, Mono-Frank-Wolfe, reduces the number of per-function gradient evaluations from $T {1/2}$ [Chen2018Online] and $T {3/2}$ [chen2018projection] to 1, and achieves a $(1-1/e)$-regret bound of $O(T {4/5})$. The second one, Bandit-Frank-Wolfe, is the first bandit algorithm for continuous DR-submodular maximization, which achieves a $(1-1/e)$-regret bound of $O(T {8/9})$. Finally, we extend Bandit-Frank-Wolfe to a bandit algorithm for discrete submodular maximization, Responsive-Frank-Wolfe, which attains a $(1-1/e)$-regret bound of $O(T {8/9})$ in the responsive bandit setting. Papers published at the Neural Information Processing Systems Conference.