Numerical Analysis

Liyao Lyu, Xinyue Yu, Hayden Schaeffer

This provides a method for modeling collective behaviors in biological systems, representing a novel approach to learning measure-dependent interactions from data.

Pierfrancesco Beneventano, Patrick Cheridito, Robin Graeber et al.

Provides a theoretical foundation for the expressive power of DNNs in high-dimensional approximation, addressing a fundamental problem in approximation theory.

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

This work addresses a major open problem in computational statistics and machine learning by enabling faster sampling algorithms for log-concave distributions, which is incremental but crucial for applications like Bayesian inference.

Francesco Regazzoni

This addresses a practical limitation in data-driven material science where full-field measurements are often inaccessible, enabling more robust material model discovery.

Samuel N. Cohen, Filippo de Feo, Jackson Hebner et al.

This work addresses infinite-dimensional PDEs and optimal control problems, which are foundational in applied sciences like physics and stochastic systems, representing a novel paradigm rather than an incremental improvement.

Junaid Aftab, Yuehaw Khoo, Haizhao Yang

This provides a foundational quantum analogue for non-uniform discrete Fourier transforms, enabling quantum algorithms for irregularly sampled data in applications like signal processing.

Guang Hao Low, Yuan Su

This work addresses a bottleneck in quantum computing for linear systems, offering significant speedups in query efficiency, particularly for initial state preparation, which is crucial for practical quantum algorithms in scientific computing.

Johannes Lang, Vincenzo Citro, Luca Leuzzi et al.

This provides a tool for physicists, economists, biologists, and computer scientists to study slow dynamics in complex landscapes, such as aging and relaxation in glassy systems, which was previously limited.

Xingyu Chen, Ruiqi Zhang, Lin Liu

It addresses a computational bottleneck for researchers and practitioners in statistics, machine learning, and computer science who rely on U-statistics, offering a more efficient solution.

Chinmay Datar, Taniya Kapoor, Abhishek Chandra et al.

For researchers solving time-dependent PDEs, this work removes the need for gradient descent and specialized hardware, enabling fast and accurate PINN training.

Radu-Alexandru Dragomir, Xiaowen Jiang, Bonan Sun et al.

This addresses a fundamental bottleneck in non-convex optimization for machine learning and scientific computing, offering a practical improvement over existing methods like perturbed gradient descent.

Shuixin Fang, Yue Qiu, Weidong Zhao

For researchers in numerical analysis and stochastic computation, this provides a foundational framework for designing high-order BSDE solvers, addressing a long-standing gap.

Sebastien Andre-Sloan, Dibyakanti Kumar, Alejandro F Frangi et al.

This provides foundational theoretical guarantees for PINNs in fluid dynamics, addressing a key bottleneck for reliable simulations in engineering and physics.

Kailiang Wu

This work addresses the need for integrated stabilization in computational fluid dynamics and related fields, offering a novel approach that is not incremental but provides a unified solution.

Yueqi Wang, Wing Tat Leung, Guanglian Li

This work addresses the challenging problem of solving Maxwell equations in heterogeneous media with high wavenumber, which is crucial for applications like metamaterial simulations, by providing a method that significantly relaxes mesh size constraints.

Angxiu Ni

Provides a new computational tool for estimating parameter derivatives in unstable stochastic systems, relevant for optimization and data assimilation.

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.

Isabel Detherage, Rikhav Shah

This work solves a longstanding open problem in numerical linear algebra by improving the theoretical understanding and stability of matrix factorization algorithms, which are foundational for computational mathematics and scientific computing.

Daniel Bach, Andrés M. Rueda-Ramírez, Eric Sonnendrücker et al.

This work provides a new methodology for constructing compatible discretizations in computational physics, particularly for problems requiring exact preservation of divergence and curl constraints.

Eky Febrianto, Yiren Wang, Burigede Liu et al.

This work addresses computational mechanics problems for researchers in quantum computing and numerical analysis, offering a method with potential exponential speedup over classical approaches.