斯坦福大学（Stanford University），全名小利兰·斯坦福大学（Leland Stanford Junior University），简称“斯坦福”，位于美国加州旧金山湾区南部帕罗奥多市境内，临近高科技园区硅谷（Silicon Valley），是私立研究型大学，全球大学高研院联盟成员。 斯坦福大学于1885年成立，1891年开始正式招生，占地约33平方公里（8180英亩），是美国占地面积最大的大学之一。斯坦福大学与旧金山北湾的加州大学伯克利分校共同构成了美国西部的学术中心，并负责运行管理SLAC国家加速器实验室、胡佛研究所等机构。据统计，截至2021年4月，共有84位斯坦福大学的校友、教授及研究人员曾获得诺贝尔奖（世界第七）、29位曾获得图灵奖（世界第一）、8位曾获得过菲尔兹奖（世界第七）。2019-20年度，斯坦福大学位列泰晤士高等教育世界大学声誉排名第3；2020-21年度，斯坦福位列U.S. News世界大学排名第3 、QS世界大学排名第2 、泰晤士高等教育世界大学排名第4、软科世界大学学术排名第2。斯坦福大学为硅谷的形成和崛起奠定了坚实的基础，培养了众多高科技公司的领导者，其中包括惠普、Google、雅虎、耐克、罗技、Snapchat、美国艺电公司、太阳微、NVIDIA、思科及LinkedIn等公司的创办人。 此外，斯坦福的校友涵盖30名富豪企业家及17名NASA太空员，亦为培养最多美国国会成员的高等院校之一。根据研究公司Wealth-X发布的2019年大学超高净值校友排行榜，斯坦福大学名列第二，仅次于哈佛大学。
Characterizing the mechanical response of materials traditionally requires solving optimization problems in which model parameters are calibrated or trained to minimize the discrepancy between model predictions and experimental data. This process can be computationally expensive and time-consuming. To overcome this limitation, we propose two neural operator architectures that directly map experimentally measured data to the constitutive functions governing the mechanical response of the material: Physics-Augmented Neural Operators (PANO) and Constitutive Artificial Neural Operators (CANO). The proposed neural operators approximate the mapping between the infinite-dimensional input space of full-field displacement measurements and net reaction forces, and the infinite-dimensional output space of hyperelastic strain–energy density functions. The displacement fields are encoded through Laplacian eigenfunctions to obtain discretization-independent and noise-robust predictions. We constrain the output space to physically admissible material models that satisfy fundamental physical requirements by design. Here, we focus on isotropic, incompressible hyperelasticity and assume that the material properties are uniform across the specimen. The neural operators are trained on simulated data tuples of displacement fields and reaction force functions for a range of material models. Once trained, the neural operators enable near-instantaneous material characterization and require only a single forward pass to infer the strain–energy density function from a given experimental dataset. We test the predictive power of the neural operators for unseen data, noisy data, data with missing information, data from different spatial discretizations, and data from geometries of different sizes. We finally discuss the ill-posedness of the inverse material characterization problem and show that constraining the output function space of our neural operator framework sufficiently regularizes the problem. The trained neural operators enable rapid and robust discovery of polyconvex strain–energy density functions while avoiding the need to solve computationally expensive inverse problems.
What is the best compromise in a situation where different people value different things? The most common method for answering this question is to look at all the options, add up the utility per person associated with each, and pick the option with the largest sum. This approach seems like the obvious, theory-neutral solution, though, in fact, it relies on substantive utilitarian commitments. A second, quite common approach, involves integrating egalitarian concerns, and picking an option that trades off maximizing utility with equalizing outcomes. But there is an important, though often-ignored, third approach as well: a contractualist approach, which models what rational actors would agree to. In this paper, we test the proposals of these three competing preference aggregation algorithms in social decision-making contexts that are systematically sampled across a wide range. While the dominant approach to value aggregation up to now has been utilitarian, we find that participants strongly prefer the aggregations recommended by the contractualist algorithm, which also dominates the egalitarian approach across a range of parameterizations. Finally, we compare the judgments of large language models (LLMs) to those of our (human) participants, finding important misalignment between model and human preferences.
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the computation of any sparse tensor algebra expression across parallel execution units. Our algorithm generalizes parallel merging algorithms to any number of operands, and to multi-dimensional, hierarchical sparse data structures. We implement our algorithm within an existing sparse tensor algebra compilation framework to automatically generate parallel sparse tensor algebra kernels that target multi-core CPUs and GPUs. We show that our generated code is competitive with hand-implemented parallelization strategies used by vendor libraries like Intel MKL and NVIDIA cuSPARSE (geo-means of 0.73–3.4×) and Taco (geo-means of 1.0–2.4×), and significantly outperforms general-purpose strategies for sparse tensor expressions where specialized algorithms have not been developed (geo-means of 2.0–6.4×).
