Core Concepts
Asgard is built around a unified framework for representing and executing dynamical systems. At its core are three interconnected concepts: equations, circuits, and runtime.
Philosophy
Asgard is built around four core principles:
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Structure is the object of computation. Implicit models (neural ODEs, PINNs) approximate the dynamics as a black box, and classical solvers compile the equations away into trajectory-stepping code. Asgard takes a third path: it keeps the mathematical structure explicit and typed from equation to execution — so you can inspect, compose, and reason about it, not just run it.
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Typed by construction. Circuits are built from atomics with fixed input/output degrees, and composition is checked statically. Malformed systems are caught at compile time as degree mismatches, before any numerics run.
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Same circuit, different calculi. The same computational circuit can be interpreted under deterministic, stochastic, or discrete calculi without rewriting code.
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Composable and algebraic. Circuits are built from simple operations using category-theoretic composition, and rewrites justified by the categorical axioms provably preserve meaning — enabling formal reasoning and transformation.
Building Blocks
Equations
Define dynamical systems using LEAN-style mathematical notation. Express differential equations, integrals, and algebraic relations.
Circuits
Computational networks that transform streams. Build complex systems from atomic operations using composition and monoidal products.
Runtime
Execute circuits with different mathematical interpretations. Choose between deterministic, stochastic, and discrete calculi.