FlashSpread

GPU-accelerated Markovian and non-Markovian spreading processes on complex networks

FlashSpread simulates stochastic SIS, SIR, and renewal SEIR dynamics on sparse graphs. It provides CPU reference execution for correctness and development, Triton/CUDA fast paths for large workloads, adaptive Bernoulli tau-leaping, and graph-reusing ensembles with independent trajectories.

Highlights

• One scalar API. Simulator selects the Markovian or renewal family, resolves the device, owns reproducible random streams, and records a Trajectory.
• Current-rate renewal execution. Susceptible CSR traversal, log-normal hazard evaluation, and compact rate-bound partials are fused; device reductions and a finalizer select the current step's tau, then a transition kernel samples events.
• Degree-aware sparse traversal. Fused renewal execution supports thread, warp, and edge-merge CSR strategies with automatic selection for uniform and hub-heavy graphs.
• Memoryless propagation without stale rates. Built-in SIS/SIR execution performs dense node rate and sampling work while propagating influence through the changed outgoing frontier.
• Independent ensembles. A shared CSR graph drives node-major [N, R] state with one adaptive clock and random stream per replica.
• Scalable graph storage. GraphCSR stores int32 incoming CSR, keeps unit weights symbolic, reconstructs COO only on request, and builds its outgoing transpose lazily.
• Semantics-preserving dispatch. Only the exact, unmodified built-in SEIRModel enters the specialized fused scalar path; custom models and subclasses retain reference execution.

Installation

Install FlashSpread from PyPI:

python -m pip install flashspread

# Add Triton GPU kernels and NetworkX-backed graph generators
python -m pip install "flashspread[gpu,graph]"

For editable development from source:

git clone https://github.com/Shakeri-Lab/FlashSpread.git
cd FlashSpread

# CPU development environment
python -m pip install -e ".[dev]"

# CUDA development environment, including GPU tests
python -m pip install -e ".[dev,gpu]"

Package metadata requires Python 3.10 or newer, PyTorch 2.0 or newer, and NumPy 1.24 or newer. A bare import flashspread is lazy: it does not initialize PyTorch, NumPy, Triton, or the optional graph stack until an exported runtime object is used. On a CUDA-capable host, install the gpu extra or pass device="cpu" explicitly.

Extra	Dependency	Capability
gpu	triton>=2.1	Triton GPU kernels
graph	networkx>=3.0	NetworkX-backed graph generators
reorder	scipy>=1.10	reverse Cuthill-McKee preprocessing
all	all runtime extras	GPU, graph generation, and reordering
dev	pytest, Ruff, mypy, NetworkX, SciPy	development and testing

Inspect the active environment with:

import flashspread as fs

fs.check_env()

Quick start

Renewal SEIR

This example runs through the CPU reference engine on a CPU-only machine and selects the fused CUDA path when a supported GPU is available. The direct circulant graph constructor does not require NetworkX.

import flashspread as fs

graph = fs.regular_graph(
    10_000,
    degree=8,
    seed=0,
    algorithm="circulant",
)
model = fs.SEIRModel(
    beta=0.25,
    mean_ei=5.0,
    median_ei=4.0,
    mean_ir=7.5,
    median_ir=5.0,
)
config = fs.EngineConfig(epsilon=0.03, tau_max=1.0)

sim = fs.Simulator(graph, model, seed=0, config=config).seed_infection(100)
trajectory = sim.run(until=50.0, record_every=1.0)

print(trajectory.peak_infected, trajectory.peak_time)
print(trajectory.final_attack_rate)
print(trajectory["I"])

SEIRModel uses log-normal E-to-I and I-to-R holding times, so each pair must satisfy mean > median > 0. Set transmission_mode="age_dependent" to scale infectious-source shedding by the source node's current I-to-R hazard.

Markovian SIS and SIR

SIS and SIR also run on CPU or CUDA. Automatic Markovian dispatch is eager to preserve one-step granularity; CUDA Graph batching is an explicit option.

import flashspread as fs

graph = fs.regular_graph(10_000, degree=8, seed=1, algorithm="circulant")
model = fs.SISModel(beta=0.5, delta=0.2)

sim = fs.Simulator(graph, model, seed=1).seed_infection(100)
trajectory = sim.run(until=30.0)

print(trajectory.peak_infected)

To request batched Markovian execution on CUDA:

config = fs.EngineConfig(execution="cuda_graph", batch_steps=50)
sim = fs.Simulator(graph, model, device="cuda", seed=1, config=config)

Independent ensembles

The ensemble factory stores the graph once and advances independent trajectories. State, age, and rate tensors are node-major [N, R]; tau and current_time have shape [R]. CUDA selects the tiled Triton implementation, while CPU selects the PyTorch reference.

import flashspread as fs
from flashspread.engines import create_ensemble_engine

graph = fs.regular_graph(100_000, degree=8, seed=2, algorithm="circulant")
model = fs.SEIRModel(beta=0.3)
engine = create_ensemble_engine(graph, model, replicas=32, seed=2)

engine.seed_infection(100)
tau, state = engine.step()
counts = engine.count_by_state()

print(tau.shape)                  # [32]
print(state.shape)                # [100_000, 32]
print(counts.shape)               # [32, 4]

Simulator intentionally remains scalar: a single Trajectory cannot represent the ensemble engine's independently adaptive clocks.

Configuration and dispatch

EngineConfig is the preferred immutable configuration surface. Invalid combinations fail before engine allocation or CUDA Graph capture.

config = fs.EngineConfig(
    backend="auto",          # auto | reference | fused
    execution="auto",       # auto | eager | cuda_graph
    traversal="auto",       # auto | thread | warp | merge
    transmission="model",   # model | constant | age_dependent
    precision="fp32",       # fp32 | bf16_weights | mixed
    compact=False,
    batch_steps=50,
    epsilon=0.03,
    tau_max=1.0,
)

The default policy is:

Model/device	Automatic execution
SIS or SIR, CPU	eager PyTorch reference
SIS or SIR, CUDA	eager CUDA/Triton Markovian engine
exact built-in SEIR, CPU	eager PyTorch renewal reference
exact built-in SEIR, CUDA	fused renewal CUDA Graph
custom or modified renewal model	reference backend preserving model hooks

Legacy Simulator engine keywords remain supported, but a call must use either config=EngineConfig(...) or legacy engine keywords, not both. Power users can call create_markovian_engine, create_renewal_engine, create_ensemble_engine, or create_engine from flashspread.engines directly.

Active compaction is restricted to fused CUDA Graph execution with thread traversal. Mixed storage requires the fused backend and is compatible with the production traversal strategies. Graph and model parameters are construction-time inputs: rebuild the engine after changing topology, weights, model parameters, or intervention policy.

Graphs

GraphCSR is the runtime graph contract. By default, rows are target nodes and columns are source nodes whose state or infectivity contributes to that target. Directed COO input therefore uses [source, target]; undirected input must contain both directions.

import torch
import flashspread as fs

# COO: 0 -> 1 and 1 -> 0
edge_index = torch.tensor([[0, 1], [1, 0]])
graph_from_edges = fs.from_edges(edge_index, num_nodes=2)

# Incoming CSR: row 0 reads source 1; row 1 reads source 0
row_ptr = torch.tensor([0, 1, 2], dtype=torch.int32)
col_ind = torch.tensor([1, 0], dtype=torch.int32)
graph_from_csr = fs.from_csr(row_ptr, col_ind)

The public generators are symmetric by default and accept a reproducibility seed:

fs.regular_graph(1_000_000, degree=8, seed=42, algorithm="circulant")
fs.regular_graph(100_000, degree=8, seed=42)       # NetworkX random-regular
fs.barabasi_albert(100_000, m=4, seed=42)
fs.watts_strogatz(100_000, k=8, p=0.1, seed=42)
fs.geometric(100_000, radius=0.01, seed=42)

algorithm="circulant" builds an exact-simple undirected regular graph directly in int32 CSR with bounded temporary storage. It is suitable for very large deterministic workloads, but it is not a uniformly sampled random-regular graph. The other generator paths require the graph extra. Engines accept GraphCSR directly or an object whose .csr attribute is a GraphCSR.

Graph storage is immutable while an engine is bound. Use graph.with_weights(...) and construct a new engine when edge weights change.

Execution model

Markovian family

Each built-in SIS/SIR leap evaluates rates and samples events over all N nodes. After state changes, the engine updates influence by traversing the outgoing edges of the changed frontier F. Its per-leap work is therefore O(N + sum(deg_out(v) for v in F)), not sparse O(|F|).

Renewal family

Renewal hazards change with compartment age, so rates must be evaluated from the current state and age on every internal step. The specialized CUDA path is deliberately multi-phase:

1. Fuse susceptible incoming-CSR traversal, stable erfcx log-normal hazards, public current-rate writes, and compact maximum-rate partials.
2. Reduce the compact partials and finalize the adaptive tau for that same rate field.
3. Sample Bernoulli events, update state and age, and advance the clock.

CUDA Graph execution replays this sequence for a fixed batch of internal steps. Public rates remain materialized for inspection; the implementation does not claim that the whole simulation step is one monolithic kernel.

Ensemble family

Ensembles share incoming CSR metadata but retain independent state, age, adaptive time, and random streams per replica. The exact constant-transmission built-in SEIR path uses a packed infectious bitmap, tiled CSR/rate evaluation, compact per-replica reductions, and a tiled transition phase. Other supported models use the tiled gather with reference model and transition hooks.

Numerical semantics

FlashSpread uses adaptive Bernoulli tau-leaping, which is an approximation to the continuous-time process. epsilon controls the renewal per-step hazard scale; max_prob and theta control Markovian adaptation; tau_max caps one internal leap. Validate tolerance sensitivity and agreement with an exact reference for the model and observable of interest. No universal error floor is claimed for the current-rate implementation.

run(until=...) stops after the first completed internal step or CUDA Graph window at or beyond the requested horizon. trajectory.times[-1] is the actual end time. Eager execution gives one-step granularity; smaller batch_steps gives tighter batched granularity. The fused scalar CUDA Graph engine double-buffers and rounds an odd requested batch size up to the next even value; inspect sim.steps_per_launch for the effective window.

reset() reproduces the base random stream. reset(episode=k) derives an independent episode stream from base_seed + k. Engine-owned model parameters are copied at construction, so mutating the original model does not update a running simulation.

Performance snapshot

The latest production-path acceptance run used one NVIDIA A100-SXM4-80GB, Python 3.12.2, PyTorch 2.11.0+cu130 with its CUDA 13.0 build/runtime, and Triton 3.6.0. Scalar workloads used N=1,000,000, approximately 8,000,000 directed CSR entries, and 50 internal steps per timed Simulator.step() call. The ensemble used the same regular graph with R=32 and timed one independent-replica step.

Workload	Early	Peak	Late	Metric
Renewal, constant transmission	12.421	13.665	15.576	G-NUPS
Renewal, age-dependent transmission	11.410	12.223	14.029	G-NUPS
Renewal, mixed storage	12.752	13.957	16.298	G-NUPS
Barabasi-Albert m=4, auto/merge	2.181	2.757	3.676	G-NUPS
Markovian SIS	15.548	13.931	14.234	G-NUPS
Ensemble SEIR, R=32	11.824	11.612	15.250	G node-replica updates/s

For scalar runs, NUPS is N * internal tau-leaps / target wall time; it is not the number of realized transitions, frontier edges, or unique changed nodes. Ensemble throughput is N * R / step wall time.

Early, peak, and late are deterministic synthetic checkpoints restored independently before each target, not phases observed along one simulated trajectory. Renewal checkpoint fractions (S, E, I, R) are (0.98, 0.01, 0.01, 0), (0.45, 0.15, 0.25, 0.15), and (0.05, 0.02, 0.03, 0.90); SIS infected fractions are 0.01, 0.25, and 0.03. Regular cases use a seeded exact-simple circulant, not a uniform random-regular sample. Timings exclude construction, checkpoint restoration, and warmup.

These are synchronized wall-time measurements, not a hardware-counter roofline result. The available Nsight Compute run lacked GPU performance-counter permission, so no compute-bound or memory-bound classification is asserted.

Reproducing the acceptance runs

The production harnesses record invocation, environment, graph semantics, checkpoint definitions, source fingerprints, warmup policy, and timing distributions in JSON.

# Scalar renewal: regular constant/age/mixed and BA auto-dispatch
python experiments/benchmark_acceptance.py walltime --case regular-constant
python experiments/benchmark_acceptance.py walltime --case regular-age
python experiments/benchmark_acceptance.py walltime --case regular-mixed
python experiments/benchmark_acceptance.py walltime --case ba-auto

# Captured Markovian SIS
python experiments/benchmark_markovian.py walltime

# R=32 shared-graph ensemble
python experiments/benchmark_ensemble.py walltime --replicas 32

Use --dry-run --output - to validate a command and emit provenance without requiring a GPU. Each harness also has a profile mode for one NVTX-delimited production call and a print-ncu-command mode for generating a profiler command.

The performance models in experiments/perf_model.py and experiments/ensemble_perf_model.py report logical algorithmic traffic and storage. They do not substitute for measured HBM counters.

Testing

python -m pytest
python -m pytest -m gpu       # requires an installed [gpu] extra and CUDA device

ruff check flashspread tests \
  experiments/benchmark_acceptance.py \
  experiments/benchmark_markovian.py \
  experiments/benchmark_ensemble.py \
  experiments/perf_model.py \
  experiments/ensemble_perf_model.py

CUDA/Triton tests skip automatically when a GPU is unavailable. The latest complete local run reports 347 passed, 45 skipped; the final selected A100 validation reports 73 passed.

Citation

@article{shakeri2026flashspread,
  title={FlashSpread: IO-Aware GPU Simulation of Non-Markovian Epidemic Dynamics via Kernel Fusion},
  author={Shakeri, Heman and Moradi-Jamei, Behnaz and Vajdi, Aram and Ardjmand, Ehsan},
  journal={arXiv preprint arXiv:2604.22092},
  year={2026}
}

License

FlashSpread is released under the MIT License.

Acknowledgments

This work builds on the Generalized Epidemic Modeling Framework (GEMF) and incorporates I/O-aware design principles inspired by FlashAttention.