Yuanzhe Wang

Yuanzhe Wang, Alexandre M. Tartakovsky

We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in the observations and PDE and surrogate models. First, we use the surrogate model to formulate a minimization problem in the reduced space for the maximum a posteriori (MAP) inverse solution. Then, we randomize the MAP objective function and obtain samples of the posterior distribution by minimizing different realizations of the objective function. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation with an unknown space-dependent diffusion coefficient. Among other problems, this equation describes groundwater flow in an unconfined aquifer. Depending on the training dataset and ensemble sizes, the proposed method provides similar or more descriptive posteriors of the parameters and states than the iterative ensemble smoother method. Deep ensembling underestimates uncertainty and provides less informative posteriors than the other two methods.

Yuanzhe Wang, Tian Zhi, Zihang Wei et al.

Multi-Agent Path Finding (MAPF) is a coordination problem that requires computing globally consistent, collision-free trajectories from individual start positions to assigned goal positions under combinatorial planning complexity. In dense environments, suboptimal initial plans induce compound conflicts that hinder feasible repair. For repair-based solvers like LNS2, initial plan quality critically affects downstream repair, yet this factor remains underexplored. We propose DiffLNS, a hybrid framework that integrates a discrete denoising diffusion probabilistic model (D3PM) with LNS2. The D3PM serves as an initializer with sparse social attention that learns a spatiotemporal prior over coordinated multi-agent action trajectories from expert demonstrations and samples multiple joint plans. Operating directly on the categorical action space, our discrete diffusion preserves the MAPF action structure and samples from a multimodal joint-plan distribution to produce diverse drafts well suited for neighborhood repair. These drafts act as warm starts for downstream repair, which completes unfinished trajectories and resolves remaining conflicts under hard MAPF constraints. Experimental results show that despite being trained only on instances with at most 96 agents, the initializer generalizes to scenarios with up to 312 agents at inference time. Across 20 complex and congested settings, DiffLNS achieves an average success rate of 95.8%, outperforming the strongest tested baseline by 9.6 percentage points and matching or exceeding all baselines in all 20 settings. To the best of our knowledge, this is the first work to leverage discrete diffusion for warm-starting an LNS-based MAPF solver.

Jun Zhang, Huayang Zhuge, Yiyao Liu et al.

Simultaneous Localization and Mapping (SLAM) is moving towards a robust perception age. However, LiDAR- and visual- SLAM may easily fail in adverse conditions (rain, snow, smoke and fog, etc.). In comparison, SLAM based on 4D Radar, thermal camera and IMU can work robustly. But only a few literature can be found. A major reason is the lack of related datasets, which seriously hinders the research. Even though some datasets are proposed based on 4D radar in past four years, they are mainly designed for object detection, rather than SLAM. Furthermore, they normally do not include thermal camera. Therefore, in this paper, NTU4DRadLM is presented to meet this requirement. The main characteristics are: 1) It is the only dataset that simultaneously includes all 6 sensors: 4D radar, thermal camera, IMU, 3D LiDAR, visual camera and RTK GPS. 2) Specifically designed for SLAM tasks, which provides fine-tuned ground truth odometry and intentionally formulated loop closures. 3) Considered both low-speed robot platform and fast-speed unmanned vehicle platform. 4) Covered structured, unstructured and semi-structured environments. 5) Considered both middle- and large- scale outdoor environments, i.e., the 6 trajectories range from 246m to 6.95km. 6) Comprehensively evaluated three types of SLAM algorithms. Totally, the dataset is around 17.6km, 85mins, 50GB and it will be accessible from this link: https://github.com/junzhang2016/NTU4DRadLM

Jice Zeng, Yuanzhe Wang, Alexandre M. Tartakovsky et al.

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously. We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system's hydraulic head responses.The conductivity field is represented with 706 degrees of freedom in the considered problem.The comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations' predictive posterior distribution at a fraction of the inference time of PEST-IES.