Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators, which is to correct the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction--diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction

High-Throughput Screening of Shape Memory Alloy Thin-Film Spreads using Nanoindentation

We have demonstrated the utility of nanoindentation as a rapid characterization tool for mapping shape memoryalloy compositions in combinatorial thin-film libraries. Nanoindentation was performed on Ni–Mn–Al ternary composition spreads. The indentation hardness and the reduced elastic modulus were mapped across a large fraction of the ternary phase diagram. The large shape memoryalloy composition region, located around the Heusler composition (Ni2MnAl), was found to display significant departure in these mechanical properties from the rest of the composition spread. In particular, the modulus and the hardness values are lower for the martensite region than those of the rest of the phase diagram

An Observatory Framework for Metropolitan Change: Understanding Urban Social-Ecological-Technical Systems in Texas and Beyond

In Texas and elsewhere, the looming realities of rapid population growth and intensifying effects of climate change mean that the things we rely on to live—water, energy, dependable infrastructure, social cohesion, and an ecosystem to support them—are exposed to unprecedented risk. Limited resources will be in ever greater demand and the environmental stress from prolonged droughts, record-breaking heat waves, and destructive floods will increase. Existing long-term trends and behaviors will not be sustainable. That is our current trajectory, but we can still change course. Significant advances in information communication technologies and big data, combined with new frameworks for thinking about urban places as social–ecological–technical systems, and an increasing movement towards transdisciplinary scholarship and practice sets the foundation and framework for a metropolitan observatory. Yet, more is required than an infrastructure for data. Making cities inclusive, safe, resilient, and sustainable will require that data become actionable knowledge that change policy and practice. Research and development of urban sustainability and resilience knowledge is burgeoning, yet the uptake to policy has been slow. An integrative and holistic approach is necessary to develop e ective sustainability science that synthesizes different sources of knowledge, relevant disciplines, multi-sectoral alliances, and connections to policy-makers and the public. To address these challenges and opportunities, we developed a conceptual framework for a “metropolitan observatory” to generate standardized long-term, large-scale datasets about social, ecological, and technical dimensions of metropolitan systems. We apply this conceptual model in Texas, known as the Texas Metro Observatory, to advance strategic research and decision-making at the intersection of urbanization and climate change. The Texas Metro Observatory project is part of Planet Texas 2050, a University of Texas Austin grand challenge initiative.ArchitectureOffice of the VP for Researc

Letter processing and font information during reading: beyond distinctiveness, where vision meets design

Letter identification is a critical front end of the reading process. In general, conceptualizations of the identification process have emphasized arbitrary sets of distinctive features. However, a richer view of letter processing incorporates principles from the field of type design, including an emphasis on uniformities across letters within a font. The importance of uniformities is supported by a small body of research indicating that consistency of font increases letter identification efficiency. We review design concepts and the relevant literature, with the goal of stimulating further thinking about letter processing during reading

Computational medicine, present and the future: obstetrics and gynecology perspective.

Medicine is, in its essence, decision making under uncertainty; the decisions are made about tests to be performed and treatments to be administered. Traditionally, the uncertainty in decision making was handled using expertise collected by individual providers and, more recently, systematic appraisal of research in the form of evidence-based medicine. The traditional approach has been used successfully in medicine for a very long time. However, it has substantial limitations because of the complexity of the system of the human body and healthcare. The complex systems are a network of highly coupled components intensely interacting with each other. These interactions give those systems redundancy and thus robustness to failure and, at the same time, equifinality, that is, many different causative pathways leading to the same outcome. The equifinality of the complex systems of the human body and healthcare system demand the individualization of medical care, medicine, and medical decision making. Computational models excel in modeling complex systems and, consequently, enabling individualization of medical decision making and medicine. Computational models are theory- or knowledge-based models, data-driven models, or models that combine both approaches. Data are essential, although to a different degree, for computational models to successfully represent complex systems. The individualized decision making, made possible by the computational modeling of complex systems, has the potential to revolutionize the entire spectrum of medicine from individual patient care to policymaking. This approach allows applying tests and treatments to individuals who receive a net benefit from them, for whom benefits outweigh the risk, rather than treating all individuals in a population because, on average, the population benefits. Thus, the computational modeling-enabled individualization of medical decision making has the potential to both improve health outcomes and decrease the costs of healthcare

Method of making multilayered titanium ceramic composites

A method making a titanium ceramic composite involves forming a hot pressed powder body having a microstructure comprising at least one titanium metal or alloy layer and at least one ceramic particulate reinforced titanium metal or alloy layer and hot forging the hot pressed body follwed by hot rolling to substantially reduce a thickness dimension and substantially increase a lateral dimension thereof to form a composite plate or sheet that retains in the microstructure at least one titanium based layer and at least one ceramic reinforced titanium based layer in the thickness direction of the composite plate or sheet

Adaptive energy minimisation for hp-finite element methods

This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adaptive manner. Specifically, we outline a new approach in the context of hp-adaptive finite element methods employed for the efficient numerical solution of linear and nonlinear second-order boundary value problems. Numerical experiments are presented which highlight the practical performance of this new hp-refinement technique for both one- and two-dimensional problems

An Updated Algorithm for the Generation of Neutral Landscapes by Spectral Synthesis

Background: Patterns that arise from an ecological process can be driven as much from the landscape over which the process is run as it is by some intrinsic properties of the process itself. The disentanglement of these effects is aided if it possible to run models of the process over artificial landscapes with controllable spatial properties. A number of different methods for the generation of so-called ‘neutral landscapes’ have been developed to provide just such a tool. Of these methods, a particular class that simulate fractional Brownian motion have shown particular promise. The existing methods of simulating fractional Brownian motion suffer from a number of problems however: they are often not easily generalisable to an arbitrary number of dimensions and produce outputs that can exhibit some undesirable artefacts. Methodology: We describe here an updated algorithm for the generation of neutral landscapes by fractional Brownian motion that do not display such undesirable properties. Using Monte Carlo simulation we assess the anisotropic properties of landscapes generated using the new algorithm described in this paper and compare it against a popular benchmark algorithm. Conclusion/Significance: The results show that the existing algorithm creates landscapes with values strongly correlated in the diagonal direction and that the new algorithm presented here corrects this artefact. A number of extensions of the algorithm described here are also highlighted: we describe how the algorithm can be employed to generate landscapes that display different properties in different dimensions and how they can be combined with an environmental gradient to produce landscapes that combine environmental variation at the local and macro scales

How does one become spiritual? The Spiritual Modeling Inventory of Life Environments (SMILE)

We report psychometric properties, correlates and underlying theory of the Spiritual Modeling Index of Life Environments (SMILE), a measure of perceptions of spiritual models, defined as everyday and prominent people who have functioned for respondents as exemplars of spiritual qualities, such as compassion, self-control, or faith. Demographic, spiritual, and personality correlates were examined in an ethnically diverse sample of college students from California, Connecticut, and Tennessee (N=1010). A summary measure of model influence was constructed from perceived models within family, school, religious organization, and among prominent individuals from both tradition and media. The SMILE, based on concepts from Bandura\u27s (1986) Social Cognitive Theory, was well-received by respondents. The summary measure demonstrated good 7-week test/retest reliability (r=.83); patterns of correlation supporting convergent, divergent, and criterion-related validity; demographic differences in expected directions; and substantial individual heterogeneity. Implications are discussed for further research and for pastoral, educational, and health-focused interventions