PRIYA-Simulation Emulator Overview

• PRIYA-Simulation Emulator is a dual-purpose framework combining high-fidelity Lyman‑α forest simulations with a modular, API-driven containerized runtime for simulation management.
• It employs a multi-fidelity Gaussian-process methodology to interpolate complex cosmological observables with interpolation errors below 1%, enhancing reliability in parameter inference.
• The platform streamlines simulation orchestration through REST APIs and containerization, ensuring reproducibility and scalability for diverse cosmological and infrastructure applications.

Searching arXiv for the most relevant papers on PRIYA, simulation emulators, and API-driven/containerized simulation infrastructures. PRIYA-Simulation Emulator denotes, in current usage, two closely related constructs: the PRIYA-based emulator used for Lyman-$\alpha$ forest cosmology, and a SUNRISE-inspired pattern for exposing simulation systems through a modular, API-driven, containerized runtime. In the cosmological literature, PRIYA is a suite of high-resolution cosmological hydrodynamical simulations of the intergalactic medium and the Lyman-$\alpha$ forest, together with a multi-fidelity statistical emulator that predicts the one-dimensional flux power spectrum and related summaries across cosmological and astrophysical parameter spaces (Bird et al., 2023, Fernandez et al., 2023). In the infrastructure literature, a “PRIYA-Simulation Emulator” is described as a platform inspired by SUNRISE, built around containerized systems, REST APIs, experiment state management, and distributed compute back-ends (Kraus et al., 12 Jun 2025).

1. Origins and scope

PRIYA was introduced as “a new suite of Lyman-alpha forest simulations for cosmology,” based on the code and hydrodynamic model of the ASTRID simulation and designed for cosmological analyses of the Lyman-$\alpha$ forest. The original presentation emphasized a $9$-dimensional parameter space, $48$ low fidelity simulations with $1536^3$ particles in a $120$ Mpc/h box, and $3$ high fidelity simulations with $3072^3$ particles in the same box. It also described a Gaussian-process emulator for the 1D flux power spectrum and the mean IGM temperature, with final interpolation error $< 1\%$ and percent-level convergence for $\alpha$0–$\alpha$1 (Bird et al., 2023).

Subsequent cosmological analyses used PRIYA as the theoretical backbone for eBOSS Lyman-$\alpha$2 inference and described the practical parameter space as $\alpha$3-dimensional, comprising $\alpha$4 simulated parameters and $\alpha$5 post-processing mean-flux parameters. In that usage, PRIYA is characterized as the first suite to resolve the Lyman-$\alpha$6 forest in a $\alpha$7 volume using a multi-fidelity emulation technique, with $\alpha$8 interpolation error over the target domain (Fernandez et al., 2023). Later small-scale work on XQ100 and KODIAQ-SQUAD described the emulator in terms of $\alpha$9 low-fidelity simulations with $\alpha$0 gas particles and $\alpha$1 high-fidelity simulations with $\alpha$2 gas particles in the same $\alpha$3 volume, indicating an expanded training basis for the small-scale P1D analysis (Ho et al., 22 Sep 2025).

The infrastructure-oriented usage is distinct in purpose but similar in abstraction. There, a “PRIYA-Simulation Emulator” is presented as a platform design inspired by SUNRISE: a unified approach to simulation and emulation workloads in which heterogeneous systems are containerized, described by standardized JSON metadata, and executed through a common REST control plane (Kraus et al., 12 Jun 2025).

2. Simulation basis and emulated observables

In its cosmological form, PRIYA is built on MP-Gadget and inherits the full-physics galaxy-formation model associated with ASTRID. The simulations evolve dark matter and baryons, include star formation, stellar feedback, black-hole growth, AGN thermal feedback, self-shielding, and patchy hydrogen and helium reionization. The suite was explicitly designed to improve on earlier Lyman-$\alpha$4 simulation sets through larger particle loads, physically motivated patchy hydrogen and helium reionization, and self-consistent AGN feedback, while also containing a realistic population of DLAs (Bird et al., 2023).

The principal emulated observable is the one-dimensional Lyman-$\alpha$5 forest flux power spectrum, denoted either $\alpha$6 or $\alpha$7. In the small-scale formulation, the transmitted flux is written as $\alpha$8, the flux contrast as $\alpha$9, and the 1D flux power spectrum as the ensemble average of $9$0. PRIYA also emulates the mean IGM temperature $9$1, defined in the original suite as the median temperature of gas particles within $9$2 of the cosmic mean density (Bird et al., 2023, Ho et al., 22 Sep 2025).

The parameterization of the cosmological sector is tuned to Lyman-$9$3 scales rather than to CMB pivots. In the original suite and the later small-scale analyses, the primordial spectrum is written as

$9$4

with $9$5 and $9$6 serving as the principal small-scale amplitude and tilt parameters. Mean-flux freedom is introduced through an effective optical depth model,

$9$7

which is implemented by rescaling optical depths in post-processing rather than by rerunning the hydrodynamics (Bird et al., 2023, Ho et al., 22 Sep 2025).

A second, downstream representation of the emulated output appears in the neutrino self-interaction analysis. There the PRIYA-based emulator is not called at the level of $9$8; instead, it is encapsulated by the compressed pair $9$9, the amplitude and slope of the linear matter power spectrum at

$48$0

This compressed form is derived from the eBOSS+$48$1 chain of the PRIYA analysis and is then used as a portable likelihood in later cosmological applications (He et al., 19 Mar 2025).

3. Emulator construction and statistical form

PRIYA uses a multi-fidelity Gaussian-process strategy. In the original suite, a Gaussian process is used to interpolate to arbitrary parameter combinations, and the published construction describes separate low-fidelity and high-fidelity tiers linked by a linear multi-fidelity model. In the small-scale P1D analysis, this is written schematically as a low-fidelity GP over the training grid plus a high-fidelity correction learned from the sparse HF runs, yielding

$48$2

with the low-fidelity tier used for coverage and the high-fidelity tier used to correct resolution systematics (Bird et al., 2023, Ho et al., 22 Sep 2025).

The eBOSS likelihood analysis presents the same logic in a different algebraic form,

$48$3

where $48$4 is a redshift-dependent multiplicative coefficient and $48$5 is the additive Gaussian-process correction. That study emphasizes an $48$6-dimensional inference space, with the emulator evaluated at negligible cost once the suite has been run (Fernandez et al., 2023).

A further compression layer is used in the neutrino self-interaction work. There, the authors take the “eBOSS + $48$7” chain from Fernández et al. 2024, extract the posterior distribution of $48$8 and $48$9, and fit a 2D Gaussian to define the PRIYA-based compressed likelihood. The resulting likelihood is treated as a Gaussian prior on the model-independent amplitude and slope of the linear power spectrum at $1536^3$0 and $1536^3$1, with nuisance effects from metals, noise, resolution, damped systems, and patchy He reionization already folded into the mean and covariance (He et al., 19 Mar 2025).

Representation	Quantity	Role
Full emulator	$1536^3$2 or $1536^3$3	Direct forward model for Lyman-$1536^3$4 analyses
Thermal emulator	$1536^3$5	IGM-temperature constraint and joint inference
Compressed emulator output	$1536^3$6 at $1536^3$7	Portable Gaussian likelihood for downstream cosmology

This layered statistical structure is central to PRIYA’s identity. It allows the same hydrodynamical foundation to support direct flux-power fits, compressed cosmological likelihoods, and cross-dataset comparisons without re-running the underlying simulations.

4. Cosmological applications

PRIYA’s first major application was a reanalysis of the eBOSS DR14 Lyman-$1536^3$8 forest flux power spectrum. Using the PRIYA simulations and likelihood, the authors reported $1536^3$9 from flux power alone after removing discrepant low-redshift bins, and $120$0 when IGM temperature data were added. They also found $120$1 for flux only and $120$2 with $120$3, together with a linear power amplitude and slope at $120$4, $120$5 of $120$6 and $120$7 (Fernandez et al., 2023).

The neutrino self-interaction study used PRIYA in its compressed form. It combined the Planck CMB likelihood with the 2D Gaussian prior derived from the PRIYA emulator and obtained

$120$8

for Planck + PRIYA Lyman-$120$9 at $3$0 confidence. That analysis emphasizes that the new PRIYA-based and EFT-based eBOSS likelihoods no longer reproduce the earlier preference for large neutrino self-interactions inferred from older Lyman-$3$1 modeling, and instead prefer a negligible level of neutrino self-interaction (He et al., 19 Mar 2025).

PRIYA has also been extended to small-scale P1D cosmology using high-resolution quasar spectra. In the XQ100 and KODIAQ-SQUAD study, the emulator is used up to $3$2 at $3$3–5. The XQ100 P1D yields constraints on $3$4 at $3$5 that are consistent with PRIYA results from eBOSS DR14 and Planck CMB, while KODIAQ-SQUAD favors a significantly higher $3$6 value driven by selection bias toward high-column density absorbers. The same study finds that $3$7 is more sensitive to Lyman limit system contamination and thermal history, and that XQ100 provides stronger constraints on thermal history than eBOSS DR14 without using external IGM temperature data (Ho et al., 22 Sep 2025).

These applications establish a recurring pattern. PRIYA is used either as a direct surrogate for the full Lyman-$3$8 flux power spectrum or as a compressed interface to the small-scale linear matter spectrum. This suggests a dual role: a forward model for detailed forest inference, and a transport layer by which hydrodynamical information is imported into broader cosmological parameter estimation.

5. API-driven and containerized deployment pattern

In the infrastructure literature, a SUNRISE-inspired “PRIYA-Simulation Emulator” is described as a modular, API-driven framework that sits between users and automation tools, a heterogeneous library of simulation “systems,” and one or more container-based compute back-ends. The major components are the Runtime Manager (RM), System Storage, Compute Back-Ends, and Front-Ends. A “system” is defined as a containerized simulation platform plus a JSON-based description, the SysDef, which declares the container image, build and run commands, parameters, and result artifacts (Kraus et al., 12 Jun 2025).

The Runtime Manager functions as the single logical control plane. It reads system definitions from storage, creates and manages experiments, maintains state through a state machine such as created $3$9 built $3072^3$0 run $3072^3$1 finished/failed, chooses a compute back-end, and exposes the EvalAPI as a REST interface. Front-ends may be a web UI, CLI, Python client, custom GUI, or CI/CD plugin. Compute back-ends may be a local Docker daemon, an on-prem cluster with container support, or Kubernetes in the cloud (Kraus et al., 12 Jun 2025).

Component	Function	Interface element
Runtime Manager	Orchestration and experiment state	EvalAPI
System Storage	Versioned system definitions	SysDef / SysAPI
Compute Back-End	Container execution	Docker API or Kubernetes API

The workflow is technology-agnostic: set up an experiment, configure and build, configure and run, analyze artifacts, and archive the experiment for reproducibility. Representative REST endpoints include POST /session, POST /session/{session_id}/parameter, POST /session/{session_id}/build, POST /session/{session_id}/run, GET /session/{session_id}/status, and GET /session/{session_id}/result/{name} (Kraus et al., 12 Jun 2025).

The same source proposes a PRIYA-specific extension in which the core orchestrator is renamed the PRIYA Runtime Manager, the schema becomes a PriyaSysDef, and the external interface becomes a PriyaEvalAPI. It also proposes, as extensions rather than as established SUNRISE features, additions such as GET /systems, GET /systems/{name}, DELETE /session/{id}, capability tags for GPU or FPGA back-ends, and authentication layers such as OAuth2 bearer tokens or mTLS (Kraus et al., 12 Jun 2025). This suggests a general way to package emulator-backed scientific simulations as portable, reproducible services.

6. Accuracy, limitations, and relation to broader emulator research

PRIYA’s published accuracy claims are stringent by Lyman-$3072^3$2 standards. The original suite reports final interpolation error $3072^3$3 and percent-level convergence for the flux power spectrum over $3072^3$4–$3072^3$5 (Bird et al., 2023). The eBOSS analysis describes $3072^3$6 interpolation error over the $3072^3$7-dimensional parameter space relevant to that likelihood (Fernandez et al., 2023). The later small-scale study reports median interpolation error $3072^3$8 for $3072^3$9–$< 1\%$0 at $< 1\%$1, rising to $< 1\%$2 at $< 1\%$3, together with resolution-convergence errors of $< 1\%$4 up to $< 1\%$5 and $< 1\%$6 at $< 1\%$7–$< 1\%$8 (Ho et al., 22 Sep 2025).

The main limitations are also explicit. In the compressed-likelihood usage, the PRIYA block carries only two numbers, $< 1\%$9 and $\alpha$00, at one pivot scale and one pivot redshift; any model dependence beyond the mapping $\alpha$01 is discarded (He et al., 19 Mar 2025). In the small-scale high-resolution analyses, LLS and HCD contamination remain a dominant nuisance, and the KODIAQ-SQUAD case shows that selection bias toward absorber-rich sightlines can overwhelm a nominal cosmological interpretation (Ho et al., 22 Sep 2025). In the deployment architecture, SUNRISE explicitly assumes non-interactive runs, single-host execution for each simulation, and leaves sophisticated scheduling, quotas, security, and access control largely outside the proof-of-concept core (Kraus et al., 12 Jun 2025).

PRIYA also sits within a wider emulator landscape. Probabilistic neural emulator networks for likelihood-free inference replace hand-designed ABC distances with learned synthetic likelihoods $\alpha$02, using local and global emulators together with acquisition rules such as MaxVar and MaxMI (Lueckmann et al., 2018). Field-level neural network emulators for cosmological $\alpha$03-body simulations predict nonlinear displacement and velocity fields directly and achieve accurate statistics down to $\alpha$04, while later survey-scale tests report agreement with $\alpha$05-body summary statistics at the $\alpha$06 level and generation times that are a thousandth of full $\alpha$07-body cost at $\alpha$08 (Jamieson et al., 2022, Scoggins et al., 18 Feb 2025). Multi-fidelity Gaussian-process work such as the Recursive Non-Additive emulator emphasizes closed-form posterior mean and variance together with active learning strategies that optimize fidelity selection under a cost budget (Heo et al., 2023).

Within that broader context, PRIYA is notable for coupling emulator methodology to a full-physics hydrodynamical forward model of the Lyman-$\alpha$09 forest, and for supporting both direct cosmological inference and aggressive compression into portable likelihoods. The SUNRISE-inspired deployment pattern, while conceptually separate, points toward a natural systems interpretation: emulator-backed simulations can be packaged as versioned, API-addressable, containerized scientific services without changing the underlying physics model (Kraus et al., 12 Jun 2025).