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Particle-based Bayesian inference methods by sampling from a partition-free target (posterior) distribution, e.g., Stein variational gradient descent (SVGD), have attracted significant attention. We propose a path-guided particle-based sampling (PGPS) method based on a novel Logweighted Shrinkage (LwS) density path linking an initial distribution to the target distribution. We propose to utilize a Neural network to learn a vector field motivated by the Fokker-Planck equation of the designed density path. Particles, initiated from the initial distribution, evolve according to the ordinary differential equation defined by the vector field. The distribution of these particles is guided along a density path from the initial distribution to the target distribution. The proposed LwS density path allows for an efficient search of modes of the target distribution while canonical methods fail. We theoretically analyze the Wasserstein distance of the distribution of the PGPS-generated samples and the target distribution due to approximation and discretization errors. Practically, the proposed PGPS-LwS method demonstrates higher Bayesian inference accuracy and better calibration ability in experiments conducted on both synthetic and real-world Bayesian learning tasks, compared to baselines, such as SVGD and Langevin dynamics, etc. 

The martensitic transformation in NiTi-based Shape Memory Alloys (SMAs) provides a basis for shape memory effect and superelasticity, thereby enabling applications requiring solid-state actuation and large recoverable shape changes upon mechanical load cycling. In order to tailor the transformation to a particular application, the compositional dependence of properties in NiTi-based SMAs, such as martensitic transformation temperatures and hysteresis, has been exploited. However, the compositional design space is large and complex, and experimental studies are expensive. In this work, we develop an interpretable piecewise linear regression model that predicts the parameter, a measure of compatibility between austenite and martensite phases, and an (indirect) factor that is well-correlated with martensitic transformation hysteresis, based on the chemical features derived from the alloy composition. The model is capable of predicting, for the first time, the type of martensitic transformation for a given alloy chemistry. The proposed model is validated by experimental data from the literature as well as in-house measurements. The results show that the model can effectively distinguish between B19 and regions for any given composition in NiTi-based SMAs and accurately estimate the lambda_2 parameter. 

We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to O(3) group and invariance to crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS). 

By querying approximate surrogate models of different fidelity as available information sources, Multi-Fidelity Bayesian Optimization (MFBO) aims at optimizing unknown functions that are costly or infeasible to evaluate. Existing MFBO methods often assume that approximate surrogates have consistently high or low fidelity across the input domain. However, approximate evaluations from the same surrogate can have different fidelity at different input regions due to data availability and model constraints, especially when considering machine learning surrogates. In this work, we investigate MFBO when multi-fidelity approximations have input-dependent fidelity. By explicitly capturing input dependency for multi-fidelity queries in a Gaussian Process (GP), our new input-dependent MFBO (iMFBO) with learnable noise models better captures the fidelity of each information source in an intuitive way. We further design a new acquisition function for iMFBO and prove that the queries selected by iMFBO have higher quality than those by naive MFBO methods, with a derived sub-linear regret bound. Experiments on both synthetic and real-world data demonstrate its superior empirical performance. 

Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph representation learning. Specifically, constructing graphs that effectively capture the complete geometric information of crystals and handle chiral crystals remains an unsolved and challenging problem. In this paper, we introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom, enabling efficient and expressive graph representations of crystals. Furthermore, we propose ComFormer, a SE(3) transformer designed specifically for crystalline materials. ComFormer includes two variants: iComFormer that employs invariant geometric descriptors of Euclidean distances and angles, and eComFormer that utilizes equivariant vector representations. Experimental results demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks across three widely-used crystal benchmarks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).