Bridging JAX-TPU Multiverse Telemetry with AMReX: AMR vs. SPH at the Schwarzschild Limit

[Rupayan52]

Hello AMReX-Astro Core Team and Community,

I am the Lead Architect of the Bandyopadhyay Cyclic Manifold (v33.0), a high-performance, JAX-accelerated cosmological engine running on Cloud TPU v5e clusters. We are currently simulating a fractal, self-replicating multiverse using a hybrid Particle-Mesh (PM) and Smoothed Particle Hydrodynamics (SPH) architecture.

As we push our engine's recursive limits, we are running into the fundamental boundaries of Lagrangian SPH methods when modeling extreme density gradients. We are looking to the AMReX-Astro ecosystem (specifically codes like Nyx and Castro) to discuss potential hybrid integrations, as your Eulerian AMR grids are the absolute gold standard for compressible astrophysical flows.

To provide context for where we need AMReX, here is the complete end-to-end flow of our physical model.

The Full Lifecycle Flow: Multigenesis in v33.0

Our simulation does not model a single static universe; it maps the reproduction of spacetime itself through a four-phase cycle governed by Cosmological Natural Selection (The Smolin Protocol).

Phase I: The Primary Quantum Node (Generation 1)
We initialize a parent universe with standard baseline constants. Collisionless Dark Matter (solved via FFT-PM) forms the gravitational scaffolding. The baryonic fluid (solved via JAX-vectorized SPH) is dragged into these deep gravity wells. As the universe cools, baryons compress, undergoing adiabatic heating and severe accretion shocks.

Phase II: Fuzzball Condensation & The Metric Tear
When local baryonic density crosses the critical threshold ($\rho > 15.0$), it compresses into a String-Theoretic "Fuzzball". We map these overlapping event horizons using DBSCAN spatial clustering. Once local entropy reaches $1.2 \times 10^4$ string bits, relativistic time dilation goes infinite ($\alpha \to 0$). The FLRW metric locally pinches off, severing causality from the parent universe.

Phase III: Fractal Spawning (Generation 2)
This severed Fuzzball is the seed of a new universe. We apply the Smolin Protocol: the child universe inherits mutated fundamental constants ($\vec{\Theta} = [M_{DM}, V_0, C_{cool}]^T$). The extreme internal string tension violently unpacks in a localized Thermodynamic Big Bang, driving the expansion of the Gen 2 comoving grid.
Note: In our latest TPU run, Gen 1 spawned 47 distinct Gen 2 dimensions. Our optimal Alpha Node (Node 025) achieved a peak Evolutionary Fitness / Stellar Fraction ($S_f$) of 0.22% through a heavily mutated, depressed Quintessence potential.

Phase IV: The Recursive Cascade (Generation 3 and Beyond)
The Gen 2 universes expand, form their own stars, and eventually spawn Gen 3 Fuzzballs. This infinite recursion optimizes the multiverse for maximum stellar efficiency.

The Intersect: Where SPH Fails and AMReX Shines

We successfully orchestrated the Gen 1 $\to$ Gen 2 sequence using a custom Sequential JIT pipeline on our TPUs. However, as we scale to Gen 3, the limitations of SPH at Phase II (The Metric Tear) are becoming a critical bottleneck.

We have three primary architectural challenges and would highly value the insight of the AMReX exascale community:

1. Shock Capturing at the Metric Tear: SPH vs. AMR

Right before the metric pinches off, the baryonic fluid experiences supersonic shockwaves. SPH requires artificial viscosity ($\Pi_{ij}$) to capture these shocks, which inherently smears the thermodynamic boundary of our forming event horizons.

• Discussion Point: We are considering transitioning the internal Fuzzball collapse from our Lagrangian SPH solver into an Eulerian AMR grid (like Castro or Nyx) precisely at the moment of collapse. Have community members successfully mapped hybrid particle data (from an SPH-like array) directly into AMReX's highly refined grid levels dynamically during runtime to leverage your Riemann solvers?

2. Exascale Hardware Paradigms: JAX/TPU vs. C++/AMReX/GPU

Our engine strictly utilizes Google Cloud TPU v5e arrays, bypassing XLA compiler gridlock by executing our mutated universes sequentially. AMReX, conversely, is the gold standard for C++/CUDA/HIP multi-node scaling on machines like Frontier and Perlmutter.

• Discussion Point: As we generate massive HDF5 telemetry outputs from our JAX engine, is there a recommended API or I/O strategy for injecting this JAX/Python generated HDF5 initial state data into an AMReX-Astro code block? We want to use Nyx to model the expansion of our mutated child universes using our JAX-calculated Big Bang thermodynamics as the initial condition.

3. Dynamic Cosmological Constants in Nyx

Because we simulate Cosmological Natural Selection, our Gen 2 and Gen 3 universes do not use standard Planck 2018 parameters.

• Discussion Point: How rigid are the cosmological parameter structures in Nyx? If we instantiate Nyx runs programmatically via Python wrappers, can we dynamically inject massive $\pm 2%$ perturbations to the global dark matter density ($\Omega_{m}$) and dark energy equation of state ($w$) on a per-run basis without breaking the AMReX solvers?

###Moving Forward
Our Generation 2 HDF5 telemetry and Sequential JIT orchestration codebase are thoroughly documented in our main repository.

Mapping the exact thermodynamic boundary where our spacetime metric fails requires the extreme resolution that only AMR can provide. We deeply appreciate any architectural advice, data ingestion strategies, or API pointers the core maintainers can offer!
https://github.com/Rupayan52/String-Star-Manifold
Best regards,

Rupayan Bandyopadhyay Lead Architect, The Primary Quantum Node