Integer Linear Programming Preprocessing for Maximum Satisfiability

The Maximum Satisfiability problem (MaxSAT) is a major optimization challenge with numerous practical applications. In recent MaxSAT evaluations, most MaxSAT solvers have adopted an ILP solver as part of their portfolios. This paper investigates the impact of Integer Linear Programming (ILP) preprocessing techniques on MaxSAT solving. Experimental results show that ILP preprocessing techniques help WMaxCDCL-OpenWbo1200, the winner of the MaxSAT evaluation 2024 in the unweighted track, solve 15 additional instances. Moreover, current state-of-the-art MaxSAT solvers heavily use an ILP solver in their portfolios, while our proposed approach reduces the need to call an ILP solver in a portfolio including WMaxCDCL or MaxCDCL.

Deep Generative Data Assimilation in Multimodal Setting

Robust integration of physical knowledge and data is key to improve computational simulations, such as Earth system models. Data assimilation is crucial for achieving this goal because it provides a systematic framework to calibrate model outputs with observations, which can include remote sensing imagery and ground station measurements, with uncertainty quantification. Conventional methods, including Kalman filters and variational approaches, inherently rely on simplifying linear and Gaussian assumptions, and can be computationally expensive. Nevertheless, with the rapid adoption of data-driven methods in many areas of computational sciences, we see the potential of emulating traditional data assimilation with deep learning, especially generative models. In particular, the diffusion-based probabilistic framework has large overlaps with data assimilation principles: both allows for conditional generation of samples with a Bayesian inverse framework. These models have shown remarkable success in text-conditioned image generation or image-controlled video synthesis. Likewise, one can frame data assimilation as observation-conditioned state calibration. In this work, we propose SLAMS: Score-based Latent Assimilation in Multimodal Setting. Specifically, we assimilate in-situ weather station data and ex-situ satellite imagery to calibrate the vertical temperature profiles, globally. Through extensive ablation, we demonstrate that SLAMS is robust even in low-resolution, noisy, and sparse data settings. To our knowledge, our work is the first to apply deep generative framework for multimodal data assimilation using real-world datasets; an important step for building robust computational simulators, including the next-generation Earth system models. Our code is available at: https://github.com/yongquan-qu/SLAMS

Branching Strategy Selection Approach Based on Vivification Ratio

The two most effective branching strategies LRB and VSIDS perform differently on different types of instances. Generally, LRB is more effective on crafted instances, while VSIDS is more effective on application ones. However, distinguishing the types of instances is difficult. To overcome this drawback, we propose a branching strategy selection approach based on the vivification ratio. This approach uses the LRB branching strategy more to solve the instances with a very low vivification ratio. We tested the instances from the main track of SAT competitions in recent years. The results show that the proposed approach is robust and it significantly increases the number of solved instances. It is worth mentioning that, with the help of our approach, the solver Maple\_CM can solve more than 16 instances for the benchmark from the 2020 SAT competition.