arXiv subjects

John Anderson

Publications and source records attributed to John Anderson.

At least 19 recordsLinked to original sources

arXiv2026

Evaluating Artificial Intelligence Through a Christian Understanding of Human Flourishing

Artificial intelligence (AI) alignment is fundamentally a formation problem, not only a safety problem. As Large Language Models (LLMs) increasingly mediate moral deliberation and spiritual inquiry, they do more than provide information; they function as instruments of digital catechesis, actively shaping and ordering human understanding, decision-making, and moral reflection. To make this formative influence visible and measurable, we introduce the Flourishing AI Benchmark: Christian Single-Turn (FAI-C-ST), a framework designed to evaluate Frontier Model responses against a Christian understanding of human flourishing across seven dimensions. By comparing 20 Frontier Models against both pluralistic and Christian-specific criteria, we show that current AI systems are not worldview-neutral. Instead, they default to a Procedural Secularism that lacks the grounding necessary to sustain theological coherence, resulting in a systematic performance decline of approximately 17 points across all dimensions of flourishing. Most critically, there is a 31-point decline in the Faith and Spirituality dimension. These findings suggest that the performance gap in values alignment is not a technical limitation, but arises from training objectives that prioritize broad acceptability and safety over deep, internally coherent moral or theological reasoning.

cs.AI↗

arXiv2025

The Spheres Dataset: Multitrack Orchestral Recordings for Music Source Separation and Information Retrieval

This paper introduces The Spheres dataset, multitrack orchestral recordings designed to advance machine learning research in music source separation and related MIR tasks within the classical music domain. The dataset is composed of over one hour recordings of musical pieces performed by the Colibr\`i Ensemble at The Spheres recording studio, capturing two canonical works - Tchaikovsky's Romeo and Juliet and Mozart's Symphony No. 40 - along with chromatic scales and solo excerpts for each instrument. The recording setup employed 23 microphones, including close spot, main, and ambient microphones, enabling the creation of realistic stereo mixes with controlled bleeding and providing isolated stems for supervised training of source separation models. In addition, room impulse responses were estimated for each instrument position, offering valuable acoustic characterization of the recording space. We present the dataset structure, acoustic analysis, and baseline evaluations using X-UMX based models for orchestral family separation and microphone debleeding. Results highlight both the potential and the challenges of source separation in complex orchestral scenarios, underscoring the dataset's value for benchmarking and for exploring new approaches to separation, localization, dereverberation, and immersive rendering of classical music.

eess.AS↗

arXiv2025

High-resolution simulations unravel intensification mechanisms of pyrocumulonimbus clouds

Pyrocumulonimbus (pyroCb) firestorms -- wildfire-generated thunderstorms -- can trigger rapid fire spread. However, the multi-physics nature of pyroCb has made their core mechanisms inaccessible to direct observation and previous simulation and prediction efforts. We introduce a new simulation capability with the first high-resolution, fully coupled simulations of a pyroCb, allowing us to unravel its life cycle governed by two opposing mechanisms. We show fuel moisture is an energy sink that attenuates fire intensity rather than fueling clouds, resolving a long-standing debate. Conversely, we identify the driver of rapid intensification: the Self-Amplifying Fire-Induced Recirculation (SAFIR) mechanism, where precipitation-induced downdrafts intensify the parent fire under weak winds. This work provides a new mechanistic framework for pyroCb prediction and demonstrates a transformative computational approach for previously intractable problems in environmental science.

physics.ao-ph↗

arXiv2025

Shock formation in 1D conservation laws I: Inviscid structure

We study the stability and structure of shock formation in 1D hyperbolic conservation laws. We show that shock formation is stable near shocking simple waves: perturbations form a shock nearby in spacetime. We also characterize the boundary of the classical development in a spacetime neighborhood of the first time singularity. Finally, we describe the precise nature of nondegenerate shock formation through an expansion in homogeneous functions of fractional degree. We use these results in a companion paper to study the vanishing viscosity limit near shock formation.

math.AP↗

arXiv2025

Shock formation in 1D conservation laws II: Vanishing viscosity

We study the effects of weak viscosity on shock formation in 1D hyperbolic conservation laws. Given an inviscid solution that forms a nondegenerate shock, we add a small viscous regularization and study the limit as the viscosity vanishes. Using a matched asymptotic expansion, we determine the sharp rate of convergence in strong norms up to the time of inviscid shock formation, and we identify universal viscous behavior near the first singularity. To treat the complex interactions between multiple characteristics and the viscosity, we develop an approximation scheme that exploits a certain decoupling between shocking and nonshocking characteristics. Our analysis makes minimal assumptions on the equation, and in particular applies to the compressible Navier--Stokes equations with degenerate physical viscosity.

math.AP↗

arXiv2024

Regional climate risk assessment from climate models using probabilistic machine learning

Effective climate risk assessment is hindered by the resolution gap between coarse global climate models and the fine-scale information needed for regional decisions. We introduce GenFocal, an AI framework that generates statistically accurate, fine-scale weather from coarse climate projections, without requiring paired simulated and observed events during training. GenFocal synthesizes complex and long-lived hazards, such as heat waves and tropical cyclones, even when they are not well represented in the coarse climate projections. It also samples high-impact, rare events more accurately than leading methods. By translating large-scale climate projections into actionable, localized information, GenFocal provides a powerful new paradigm to improve climate adaptation and resilience strategies.

cs.LG↗

arXiv2024

Dynamical-generative downscaling of climate model ensembles

Regional high-resolution climate projections are crucial for many applications, such as agriculture, hydrology, and natural hazard risk assessment. Dynamical downscaling, the state-of-the-art method to produce localized future climate information, involves running a regional climate model (RCM) driven by an Earth System Model (ESM), but it is too computationally expensive to apply to large climate projection ensembles. We propose a novel approach combining dynamical downscaling with generative artificial intelligence to reduce the cost and improve the uncertainty estimates of downscaled climate projections. In our framework, an RCM dynamically downscales ESM output to an intermediate resolution, followed by a generative diffusion model that further refines the resolution to the target scale. This approach leverages the generalizability of physics-based models and the sampling efficiency of diffusion models, enabling the downscaling of large multi-model ensembles. We evaluate our method against dynamically-downscaled climate projections from the CMIP6 ensemble. Our results demonstrate its ability to provide more accurate uncertainty bounds on future regional climate than alternatives such as dynamical downscaling of smaller ensembles, or traditional empirical statistical downscaling methods. We also show that dynamical-generative downscaling results in significantly lower errors than bias correction and spatial disaggregation (BCSD), and captures more accurately the spectra and multivariate correlations of meteorological fields. These characteristics make the dynamical-generative framework a flexible, accurate, and efficient way to downscale large ensembles of climate projections, currently out of reach for pure dynamical downscaling.

physics.ao-ph↗

arXiv2024

FireBench: A High-fidelity Ensemble Simulation Framework for Exploring Wildfire Behavior and Data-driven Modeling

Background. Wildfire research uses ensemble methods to analyze fire behaviors and assess uncertainties. Nonetheless, current research methods are either confined to simple models or complex simulations with limits. Modern computing tools could allow for efficient, high-fidelity ensemble simulations. Aims. This study proposes a high-fidelity ensemble wildfire simulation framework for studying wildfire behavior, ML tasks, fire-risk assessment, and uncertainty analysis. Methods. In this research, we present a simulation framework that integrates the Swirl-Fire large-eddy simulation tool for wildfire predictions with the Vizier optimization platform for automated run-time management of ensemble simulations and large-scale batch processing. All simulations are executed on tensor-processing units to enhance computational efficiency. Key results. A dataset of 117 simulations is created, each with 1.35 billion mesh points. The simulations are compared to existing experimental data and show good agreement in terms of fire rate of spread. Computations are done for fire acceleration, mean rate of spread, and fireline intensity. Conclusions. Strong coupling between these 2 parameters are observed for the fire spread and intermittency. A critical Froude number that delineates fires from plume-driven to convection-driven is identified and confirmed with literature observations. Implications. The ensemble simulation framework is efficient in facilitating parametric wildfire studies.

physics.comp-ph↗

arXiv2023

SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models

Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble of forecasts. This is done by running many physics-based simulations under different conditions, which is a computationally costly process. We propose to amortize the computational cost by emulating these forecasts with deep generative diffusion models learned from historical data. The learned models are highly scalable with respect to high-performance computing accelerators and can sample hundreds to tens of thousands of realistic weather forecasts at low cost. When designed to emulate operational ensemble forecasts, the generated ones are similar to physics-based ensembles in important statistical properties and predictive skill. When designed to correct biases present in the operational forecasting system, the generated ensembles show improved probabilistic forecast metrics. They are more reliable and forecast probabilities of extreme weather events more accurately. While this work demonstrates the utility of the methodology by focusing on weather forecasting, the generative artificial intelligence methodology can be extended for uncertainty quantification in climate modeling, where we believe the generation of very large ensembles of climate projections will play an increasingly important role in climate risk assessment.

cs.LG↗

arXiv2023

Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models

We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to high-resolution data that is consistent with a high-fidelity scheme. Our framework tackles the problem by composing two transformations: (i) a debiasing step via an optimal transport map, and (ii) an upsampling step achieved by a probabilistic diffusion model with a posteriori conditional sampling. This approach characterizes a conditional distribution without needing paired data, and faithfully recovers relevant physical statistics from biased samples. We demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems, which are representative of the core difficulties present in numerical simulations of weather and climate. Our method produces realistic high-resolution outputs from low-resolution inputs, by upsampling resolutions of 8x and 16x. Moreover, our procedure correctly matches the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives. Code for this work is available at: https://github.com/google-research/swirl-dynamics/tree/main/swirl_dynamics/projects/probabilistic_diffusion.

cs.LG↗

arXiv2023

Multi-localized time-symmetric initial data for the Einstein vacuum equations

We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized sources of gravitational radiation, and lies in a family of data sets which is closed under scaling out the distances between the systems by arbitrarily large amounts. This class contains data sets which are not asymptotically flat, but to which nonetheless a finite ADM mass can be ascribed. The construction proceeds by a gluing scheme using the Brill--Lindquist metric as a template. Such initial data are motivated in part by a desire to understand the dynamical interaction of distant systems in the context of general relativity. As a by-product of the construction, we produce complete, scalar-flat initial data with trivial topology and infinitely many minimal spheres, as well as initial data with infinitely many Einstein--Rosen bridges.

math.DG↗

arXiv2023

Accelerating large-eddy simulations of clouds with Tensor Processing Units

Clouds, especially low clouds, are crucial for regulating Earth's energy balance and mediating the response of the climate system to changes in greenhouse gas concentrations. Despite their importance for climate, they remain relatively poorly understood and are inaccurately represented in climate models. A principal reason is that the high computational expense of simulating them with large-eddy simulations (LES) has inhibited broad and systematic numerical experimentation and the generation of large datasets for training parametrization schemes for climate models. Here we demonstrate LES of low clouds on Tensor Processing Units (TPUs), application-specific integrated circuits that were originally developed for machine learning applications. We show that TPUs in conjunction with tailored software implementations can be used to simulate computationally challenging stratocumulus clouds in conditions observed during the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS) field study. The TPU-based LES code successfully reproduces clouds during DYCOMS and opens up the large computational resources available on TPUs to cloud simulations. The code enables unprecedented weak and strong scaling of LES, making it possible, for example, to simulate stratocumulus with $10\times$ speedup over real-time evolution in domains with a $34.7~\mathrm{km} \times 53.8~\mathrm{km}$ horizontal cross section. The results open up new avenues for computational experiments and for substantially enlarging the sample of LES available to train parameterizations of low clouds.

physics.ao-ph↗

arXiv2022

A High-resolution Large-eddy Simulation Framework for Wildland Fire Predictions using TensorFlow

As the impact of wildfires has become increasingly more severe over the last decades, there is continued pressure for improvements in our ability to predict wildland fire behavior over a wide range of conditions. One approach towards this goal is through coupled fire/atmosphere modeling tools. While significant progress has been made on advancing their physical fidelity, existing modeling tools have not taken full advantage of emerging programming paradigms and computing architectures to enable high-resolution wildfire simulations. By addressing this gap, this work presents a new wildfire simulation framework that enables landscape-scale wildfire simulations with physical representation of the combustion at affordable computational cost. This is achieved by developing a coupled fire/atmosphere model in the TensorFlow programming paradigm, which enables highly efficient and scalable computations on Tensor Processing Unit (TPU) hardware architecture. To validate this simulation framework and demonstrate its efficiency, simulations of the prescribed fire experiment FireFlux II (Clements et al., 2019) are performed. By considering a parametric study on the mesh resolution, we show that the global quantities such as volumetric heat release and fire-spread rate are insensitive to the horizontal mesh resolution within a range between 0.5 m and 2 m, which is sufficient for predicting fire intermittency and dynamic fire properties associated with fine-scale turbulent structures in the atmospheric boundary layer.

physics.flu-dyn↗

arXiv2022

Global stability for nonlinear wave equations satisfying a generalized null condition

We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and improved decay of good derivatives using bilinear energy estimates and duality arguments. Combining this strategy with the $r^p$ estimates of Dafermos--Rodnianski then allows us to prove global stability. The proof requires analyzing the geometry of intersecting null hypersurfaces adapted to solutions of wave equations.

math.AP↗

arXiv2021

A TensorFlow Simulation Framework for Scientific Computing of Fluid Flows on Tensor Processing Units

A computational fluid dynamics (CFD) simulation framework for fluid-flow prediction is developed on the Tensor Processing Unit (TPU) platform. The TPU architecture is featured with accelerated dense matrix multiplication, large high bandwidth memory, and a fast inter-chip interconnect, making it attractive for high-performance scientific computing. The CFD framework solves the variable-density Navier-Stokes equation using a low-Mach approximation, and the governing equations are discretized by a finite-difference method on a collocated structured mesh. It uses the graph-based TensorFlow as the programming paradigm. The accuracy and performance of this framework is studied both numerically and analytically, specifically focusing on effects of TPU-native single precision floating point arithmetic. The algorithm and implementation are validated with canonical 2D and 3D Taylor-Green vortex simulations. To demonstrate the capability for simulating turbulent flows, simulations are conducted for two configurations, namely decaying homogeneous isotropic turbulence and a turbulent planar jet. Both simulations show good statistical agreement with reference solutions. The performance analysis shows a linear weak scaling and a superlinear strong scaling up to a full TPU v3 pod with 2048 cores.

physics.comp-ph↗

arXiv2021

Global stability for a nonlinear system of anisotropic wave equations

In this paper, we initiate the study of global stability for anisotropic systems of quasilinear wave equations. Equations of this kind arise naturally in the study of crystal optics, and they exhibit birefringence. We introduce a physical space strategy based on bilinear energy estimates that allows us to prove decay for the nonlinear problem. This uses decay for the homogeneous wave equation as a black box. The proof also requires us to interface this strategy with the vector field method and take advantage of the scaling vector field. A careful analysis of the spacetime geometry of the interaction between waves is necessary in the proof.

math.AP↗

arXiv2020

Deep Learning Models for Predicting Wildfires from Historical Remote-Sensing Data

Identifying regions that have high likelihood for wildfires is a key component of land and forestry management and disaster preparedness. We create a data set by aggregating nearly a decade of remote-sensing data and historical fire records to predict wildfires. This prediction problem is framed as three machine learning tasks. Results are compared and analyzed for four different deep learning models to estimate wildfire likelihood. The results demonstrate that deep learning models can successfully identify areas of high fire likelihood using aggregated data about vegetation, weather, and topography with an AUC of 83%.

cs.CV↗

arXiv2020

Stability and instability of traveling wave solutions to nonlinear wave equations

In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition which allows us to prove the global nonlinear asymptotic stability of the plane wave. The proof of global stability requires us to analyze the geometry of the interaction between the background plane wave and the perturbation. When this condition is not met, we are able to prove linear instability assuming an additional genericity condition. The linear instability is shown using a geometric optics ansatz.

math.AP↗