Asgard

A mathematical framework for modeling, simulating, and reasoning about dynamical systems using Linear Categorical Logic.

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Unified Framework

One system for ODEs, SDEs, PDEs, and discrete equations. Express systems in natural mathematical notation.

Multiple Calculi

Same system, different interpretations. Switch between deterministic, stochastic, and discrete calculi.

Composable Circuits

Build complex systems from simple operations. Compose, parallelize, and trace circuits algebraically.

JAX-Powered

Fast execution with automatic differentiation and GPU acceleration through JAX.

Proof System

Reason about and transform systems algebraically using rewrite rules and tactics.

LEAN-Style Syntax

Standard mathematical notation for equations. Familiar syntax for mathematicians and researchers.

Getting Started Quickly

Install Asgard and create your first circuit in minutes.

# Clone the repository
git clone https://github.com/arnovich/gimle-asgard.git
cd gimle-asgard

# Install with uv
uv sync

# Verify installation
uv run python -c "from gimle.asgard.circuit.circuit import Circuit; print('Asgard installed!')"

Or create and run a simple integration:

from gimle.asgard.circuit.circuit import Circuit
from gimle.asgard.runtime.stream import Stream, StreamState
import jax.numpy as jnp

# Create a circuit that integrates along dimension x
circuit = Circuit.from_string("register(x)")

# Input: f(x) = x (Taylor coefficients [0, 1])
input_stream = Stream(
    data=jnp.array([[0.0, 1.0]]),
    dim_labels=("x",),
    chunk_size=1
)

# Execute the circuit
outputs, state = circuit.execute([input_stream], StreamState())
print(f"Output: {outputs[0].data}")  # [0, 0, 1] representing x^2/2

Use Cases

Climate & Weather

Model complex atmospheric dynamics and simulate climate patterns.

Finance

Option pricing, risk analysis, and stochastic process simulation.

Physics & Engineering

Solve differential equations and simulate physical systems.

Research

Explore connections between computation and dynamical systems theory.

Next Steps