Numerical Analysis

Lizhang Chen, Jonathan Li, Chen Liang et al.

It provides a method to enhance frozen transformer models at test time, offering a practical way to boost performance without additional training.

Zakhar Shumaylov, Nathaël Da Costa, Peter Zaika et al.

For optimization researchers, this work demystifies the success of Muon, suggesting that geometric narratives may be overemphasized, though the findings are incremental in nature.

Yulei Liao, Yang Liu, Pingbing Ming

For researchers solving multiscale parabolic equations, this method offers improved error bounds, but the improvement is incremental over existing approaches.

Panos Tsimpos, Edoardo Calvello, Ayoub Belhadji et al.

For researchers in probabilistic inference and Bayesian methods, this work provides theoretical foundations for amortized conditioning, potentially enabling foundation models for Bayesian inference.

Wei Chen, Zhen Liu

It provides a pressure-robust method for Stokes equations on curved domains, which is an incremental improvement over existing methods for flat domains.

Edoardo Calvello, Elizabeth Carlson, Nikola Kovachki et al.

It addresses the lack of analysis for data-driven methods in data assimilation and forecasting, providing foundational theory for researchers in machine learning and dynamical systems.

Takashi Goda, Yang Liu, Raúl Tempone

For researchers in quasi-Monte Carlo methods, this offers a simpler and more efficient randomized digital net design.

Matthew S. Zhang, Jason M. Altschuler, Sinho Chewi

This resolves the computational bottleneck of finding warm starts for HMC, which is crucial for practitioners in statistics, engineering, and sciences who rely on HMC for high-dimensional sampling, though it is incremental as it builds on prior theoretical work.

Jiahe Huang, Sihan Xu, Sharvaree Vadgama et al.

This work addresses the speed-fidelity trade-off in generative models for scientific emulation, enabling high-fidelity one- and few-step dynamic generation for physics-based tasks.

Kyurae Kim, Samuel Gruffaz, Ji Won Park et al.

For researchers using Langevin Monte Carlo for sampling, this work extends theoretical guarantees to the overdamped regime, showing the exponential integrator remains stable and effective.

Lifu Wei, Yinuo Ren, Naichen Shi et al.

It provides a computationally efficient and unbiased method for inference-time guidance in diffusion models, addressing the bottleneck of repeated score/gradient evaluations.

Jialei Li, Xiaodong Liu

For researchers in inverse scattering, this work provides a theoretical uniqueness result and a practical algorithm for simultaneous reconstruction of shape and impedance, though the convexity assumption limits generality.

James Rowbottom, Nick Huang, Carola-Bibiane Schönlieb et al.

For scientists and engineers needing to place sensors for state estimation in complex, non-Gaussian systems, this work provides a theoretically principled and practically superior method.

Nathanael Tepakbong, Hanyu Hu, Chengyu Liu et al.

For researchers using PINNs to solve PDEs, this work provides a theoretically grounded method to mitigate training difficulties caused by ill-conditioned loss landscapes, with practical improvements on several benchmark problems.

Chun-Wun Cheng, Sifan Wang, Carola-Bibiane Schönlieb et al.

For researchers in scientific machine learning, CATO provides a more accurate and efficient method for solving PDEs on complex geometries, addressing key limitations of existing transformer-based operators.

Yi Zhang

For researchers in computational plasma physics, this work provides a structure-preserving discretization for Hall MHD that ensures exact conservation properties, which is an incremental improvement over existing methods.

Chenyang Wang, Weizhong Wang, Yinuo Ren et al.

This work provides a simpler, gradient-free alternative to inference-time guidance for diffusion models, reducing computational overhead and bias.

Yueyang Wang, Xili Wang, Kejun Tang et al.

For practitioners solving PDE-governed inverse problems, this framework offers a more accurate and adaptive approach that handles high-dimensional non-Gaussian posteriors and misspecified priors without manual tuning.

Anthony Chen, Robert Krasny

This work addresses computational challenges in geophysical and fluid dynamics simulations on spherical domains, representing an incremental improvement with a novel grid-based approach.

Anas Jnini, Elham Kiyani, Khemraj Shukla et al.

This work addresses the problem of slow convergence in PINNs for researchers and practitioners in scientific machine learning, offering incremental improvements through novel optimizer implementations and scaling techniques.