One-shot learning for solution operators of partial differential equations

Discovering governing equations of a physical system, represented by partial differential equations (PDEs), from data is a central challenge in a variety of areas of science and engineering. Current methods require either some prior knowledge (e.g., candidate PDE terms) to discover the PDE form, or a large dataset to learn a surrogate model of the PDE solution operator. Here, we propose the first learning method that only needs one PDE solution, i.e., one-shot learning. We first decompose the entire computational domain into small domains, where we learn a local solution operator, and then find the coupled solution via a fixed-point iteration. We demonstrate the effectiveness of our method on different PDEs, and our method exhibits a strong generalization property

EXPLAIN, EDIT, GENERATE: Rationale-Sensitive Counterfactual Data Augmentation for Multi-hop Fact Verification

Automatic multi-hop fact verification task has gained significant attention in recent years. Despite impressive results, these well-designed models perform poorly on out-of-domain data. One possible solution is to augment the training data with counterfactuals, which are generated by minimally altering the causal features of the original data. However, current counterfactual data augmentation techniques fail to handle multi-hop fact verification due to their incapability to preserve the complex logical relationships within multiple correlated texts. In this paper, we overcome this limitation by developing a rationale-sensitive method to generate linguistically diverse and label-flipping counterfactuals while preserving logical relationships. In specific, the diverse and fluent counterfactuals are generated via an Explain-Edit-Generate architecture. Moreover, the checking and filtering modules are proposed to regularize the counterfactual data with logical relations and flipped labels. Experimental results show that the proposed approach outperforms the SOTA baselines and can generate linguistically diverse counterfactual data without disrupting their logical relationships.Comment: Accepted by EMNLP2023 Main Conferenc

Fracture toughness of CTBN modified PF particleboard based on equal deflection rigidity

The fracture toughness of particleboard should be evaluated when it was intended to use in the structure system. Single edge notched beam (SENB) test method was employed to measure stress intensity factor (SIF) of the internal middle layer of the PF and CTBN modified PF particleboard. Equal deflection rigidity algorithm (EDRA) was used to homogenized the sandwich bi-material beam in order to make the test procedure match ASTM E399-2017. The results shown that the optimized CTBN addition was among 8% to 12% and the improve ratio of SIF of the particleboard middle layer was 27.27 %. Owing to the different broken mechanism, the tested fracture performance show more stability compared to the traditional internal bonding (IB) test. But the fracture test strongly depend on the notched incision morphology