About

Josh Levine is an Associate Professor in the Department of Computer Science at the University of Arizona. He holds a Ph.D. from Ohio State University, earned in 2009. His research interests include visualization, geometric modeling, topological analysis, mesh generation, and computer graphics. Levine's work focuses on developing methods and tools in these areas to advance understanding and capabilities in visual computing and geometric data analysis.

Research topics

• Computer Science
• Artificial Intelligence
• Mathematics
• Theoretical computer science
• Algorithm
• Combinatorics
• Data Mining
• Software engineering
• Programming language
• Quantum mechanics
• Physics
• Geometry

Selected publications

• Multi-Bit Quantum-Inspired Dynamics in Nonlinear Mechanical Oscillators

  Journal of Applied Mechanics · 2026-03-30

  articleSenior author

  Abstract Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics.

  PublisherDOI

• Seeing the Many: Exploring Parameter Distributions Conditioned on Features in Surrogates

  ArXiv.org · 2025-08-18

  preprintOpen access

  Recently, neural surrogate models have emerged as a compelling alternative to traditional simulation workflows. This is accomplished by modeling the underlying function of scientific simulations, removing the need to run expensive simulations. Beyond just mapping from input parameter to output, surrogates have also been shown useful for inverse problems: output to input parameters. Inverse problems can be understood as search, where we aim to find parameters whose surrogate outputs contain a specified feature. Yet finding these parameters can be costly, especially for high-dimensional parameter spaces. Thus, existing surrogate-based solutions primarily focus on finding a small set of matching parameters, in the process overlooking the broader picture of plausible parameters. Our work aims to model and visualize the distribution of possible input parameters that produce a given output feature. To achieve this goal, we aim to address two challenges: (1) the approximation error inherent in the surrogate model and (2) forming the parameter distribution in an interactive manner. We model error via density estimation, reporting high density only if a given parameter configuration is close to training parameters, measured both over the input and output space. Our density estimate is used to form a prior belief on parameters, and when combined with a likelihood on features, gives us an efficient way to sample plausible parameter configurations that generate a target output feature. We demonstrate the usability of our solution through a visualization interface by performing feature-driven parameter analysis over the input parameter space of three simulation datasets. Source code is available at https://github.com/matthewberger/seeing-the-many

  PublisherOA PDFDOI

• Analyzing Multifaceted Scientific Data with Topological Analytics (Final Technical Report)

  2025-07-19

  reportOpen access1st authorCorresponding

  This final technical report describes the activities undertaken through Department of Energy, Office of Science, Advanced Scientific Computing Research Early Career award DE-SC-0019039, “Analyzing Multifaceted Scientific Data with Topological Analytics." This report summarizes contributions made toward the research of visualization, machine learning, and topological data analysis of complex simulation data.

  PublisherOA PDFDOI

• Seeing the Many: Exploring Parameter Distributions Conditioned on Features in Surrogates

  2025-11-02

  article

  Recently, neural surrogate models have emerged as a compelling alternative to traditional simulation workflows. This is accomplished by modeling the underlying function of scientific simulations, removing the need to run expensive simulations. Beyond just mapping from input parameter to output, surrogates have also been shown useful for inverse problems: output to input parameters. Inverse problems can be understood as search, where we aim to find parameters whose surrogate outputs contain a specified feature. Yet finding these parameters can be costly, especially for high-dimensional parameter spaces. Thus, existing surrogate-based solutions primarily focus on finding a small set of matching parameters, in the process overlooking the broader picture of plausible parameters. Our work aims to model and visualize the distribution of possible input parameters that produce a given output feature. To achieve this goal, we aim to address two challenges: (1) the approximation error inherent in the surrogate model and (2) forming the parameter distribution in an interactive manner. We model error via density estimation, reporting high density only if a given parameter configuration is close to training parameters, measured both over the input and output space. Our density estimate is used to form a prior belief on parameters, and when combined with a likelihood on features, gives us an efficient way to sample plausible parameter configurations that generate a target output feature. We demonstrate the usability of our solution through a visualization interface by performing feature-driven parameter analysis over the input parameter space of three simulation datasets. Source code is available at https://github.com/matthewberger/seeing-the-many

  PublisherDOI

• Experimental realization of logical elastic bits as qubit analogues in a nonlinear oscillator

  Scientific Reports · 2025-12-29 · 1 citations

  articleOpen accessSenior author

  Nonlinear mechanical oscillators can emulate qubit analogue algebra by leveraging multiple harmonics of large‑amplitude vibrations. We realize a logical elastic bit—a room temperature mechanical analogue of a qubit—in a two‑mass oscillator joined by a conical spring whose graded stiffness generates a robust sequence of phase‑coherent harmonics. From time‑series velocity measurements, a Fourier–projection maps the response onto the complete space of in‑phase and out‑of‑phase eigenvectors. The resulting complex coefficients define a Bloch‑sphere representation in which classical superpositions are directly controllable. Moreover, we gain more control over the coefficients by pairing the Fourier harmonics in different orders. When the paired Fourier components share a frequency, the coefficients are independent of time, producing tunable states that can serve as phase-defined memory. Pairing distinct harmonics introduces a beat frequency that drives deterministic precession of the Bloch vector, realizing single‑bit rotations (e.g., Pauli‑X and Hadamard analogues) without the need of additional external input, with time as the gate clock. By splitting the spectrum into blocks, a single resonator can host several elastic bits at once. The Hilbert space grows with the number of blocks while the hardware stays the same, allowing scalable architectures that show classical non-separable correlations. A linear mass-spring model yields closed‑form eigenfrequencies and Bloch‑angle formulas that overlay measured trajectories across resonance and provide design rules for state initialization and gate timing. All operations occur at ambient conditions and require no feedback or cryogenics, establishing a simple, reproducible route to quantum‑inspired logic in macroscopic mechanics.

  PublisherOA PDFDOI

• Differentially private scale testing via rank transformations and percentile modifications

  ArXiv.org · 2025-07-04

  articleOpen access1st authorCorresponding

  We develop a class of differentially private two-sample scale tests, called the rank-transformed percentile-modified Siegel--Tukey tests, or RPST tests. These RPST tests are inspired both by recent differentially private extensions of some common rank tests and some older modifications to non-private rank tests. We present the asymptotic distribution of the RPST test statistic under the null hypothesis, under a very general condition on the rank transformation. We also prove RPST tests are differentially private, and that their type I error does not exceed the given level. We uncover that the growth rate of the rank transformation presents a tradeoff between power and sensitivity. We do extensive simulations to investigate the effects of the tuning parameters and compare to a general private testing framework. Lastly, we show that our techniques can also be used to improve the differentially private signed-rank test.

  PublisherOA PDF

• Topology Aware Neural Interpolation of Scalar Fields

  2025-11-02

  preprintOpen access

  This paper presents a neural scheme for the topology-aware interpolation of time-varying scalar fields. Given a time-varying sequence of persistence diagrams, along with a sparse temporal sampling of the corresponding scalar fields, denoted as keyframes, our interpolation approach aims at "inverting" the non-keyframe diagrams to produce plausible estimations of the corresponding, missing data. For this, we rely on a neural architecture which learns the relation from a time value to the corresponding scalar field, based on the keyframe examples, and reliably extends this relation to the non-keyframe time steps. We show how augmenting this architecture with specific topological losses exploiting the input diagrams both improves the geometrical and topological reconstruction of the non-keyframe time steps. At query time, given an input time value for which an interpolation is desired, our approach instantaneously produces an output, via a single propagation of the time input through the network. Experiments interpolating 2D and 3D time-varying datasets show our approach superiority, both in terms of data and topological fitting, with regard to reference interpolation schemes.

  PublisherOA PDFDOI

• Unveiling nonlinear phi-bit dynamics in elastic systems: Advancing quantum-inspired computing

  The Journal of the Acoustical Society of America · 2024-10-01

  articleSenior author

  Phi-bits, the classical mechanical analogs of qubits, play a pivotal role in the development of quantum-analog computing systems. Understanding the nonlinear processes governing control and interconnectivity among phi-bits is imperative for their advancement. These phi-bits, existing as acoustic waves within arrays of interconnected waveguides, exhibit a remarkable ability to maintain coherent superpositions of two states under external nonlinear driving forces. Manipulating the frequency, amplitude, and phase of external drivers allows precise control over phi-bit states. To analyze and predict the nonlinear response of phi-bits to external stimuli, we have developed a discrete element model. This model comprehensively captures various types, strengths, and orders of nonlinearities stemming from intrinsic medium coupling between waveguides and external factors like signal generators, transducers, and ultrasonic couplant assemblies. Our study unveils significant insight, highlighting how nonlinearity type, strength, order, and damping impact the complex amplitudes' modulus and phases in the coherent superposition of phi-bit states, with a notable impact on their predictability and stability, particularly at high damping levels. This investigation explores the controlled creation of phi-bits to observe the superposition of states, essential for advancing phi-bit-based quantum analogue information processing platforms.

  PublisherDOI

• Exploring multi-qubit analogue operations through acoustic wave dynamics

  The Journal of the Acoustical Society of America · 2024-10-01 · 1 citations

  articleSenior author

  Quantum computing harnesses quantum phenomena like superposition and entanglement to surpass classical computers, showing promise across various fields. Current techniques utilize qubits in quantum circuits for parallel information processing, though managing and measuring these systems poses significant challenges. We propose a novel approach to simplify executing complex quantum algorithms without relying on multiple quantum gate operations. Our method introduces logical phi-bits—classical counterparts to qubits, using nonlinear acoustic waves in an externally driven acoustic metastructure. We demonstrate that complex multi-phi-bit unitary operations, akin to those in quantum circuits, can be conducted through a single action on this metastructure. This method starkly contrasts traditional quantum computing, which requires decomposed sequences of qubit gates for equivalent operations. The phi-bit system simplifies processes that are typically complex in quantum mechanics, potentially enhancing robustness and ease of implementation. Our results indicate that phi-bits could expand computational models by merging classical wave dynamics with quantum computational principles, thereby widening the potential of computational technologies. This research advances quantum-analogue computation and introduces new prospects for utilizing wave physics in information processing, thereby challenging and expanding existing paradigms in both classical and quantum computing. [Funding: NSF grant 2204382, 2204400, and 2242925.]

  PublisherDOI

• Acoustic metamaterials for realizing a scalable multiple phi-bit unitary transformation

  AIP Advances · 2024-02-01 · 6 citations

  articleOpen accessSenior author

  The analogy between acoustic modes in nonlinear metamaterials and quantum computing platforms constituted of correlated two-level systems opens new frontiers in information science. We use an inductive procedure to demonstrate scalable initialization of and scalable unitary transformations on superpositions of states of multiple correlated logical phi-bits, classical nonlinear acoustic analog of qubits. A multiple phi-bit state representation as a complex vector in a high-dimensional, exponentially scaling Hilbert space is shown to correspond with the state of logical phi-bits represented in a low-dimensional linearly scaling physical space of an externally driven acoustic metamaterial. Manipulation of the phi-bits in the physical space enables the implementation of a non-trivial multiple phi-bit unitary transformation that scales exponentially. This scalable transformation operates in parallel on the components of the multiple phi-bit complex state vector, requiring only a single physical action on the metamaterial. This work demonstrates that acoustic metamaterials offer a viable path toward achieving massively parallel information processing capabilities that can challenge current quantum computing paradigms.

  PublisherOA PDFDOI

Recent grants

• CGV: Large: Collaborative Research: Coupling Simulation and Mesh Generation using Computational Topology

  NSF · $350k · 2013–2016

• CGV: Large: Collaborative Research: Coupling Simulation and Mesh Generation using Computational Topology

  NSF · $192k · 2016–2018

• III: Small: Collaborative Research: Neural Volume Visualization

  NSF · $199k · 2020–2024

Frequent coauthors

• Julien Tierny

  56 shared

• Jonas Lukasczyk

  Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

  32 shared

• Charles Gueunet

  31 shared

• Maxime Soler

  Centre National de la Recherche Scientifique

  28 shared

• Daisuke Sakurai

  Fujitsu (Japan)

  28 shared

• Guillaume Favelier

  Kyushu University

  27 shared

• Christoph Garth

  University of Koblenz and Landau

  24 shared

• Peer‐Timo Bremer

  Lawrence Livermore National Laboratory

  21 shared