Mathematical Modeling After Moore's Law
From my new book: AI Powered Digital Twins (soon- Wiley 2026)
For decades, Moore’s law provided mathematical modeling with a stable computational foundation: steady gains in transistor density, clock speed, and cost efficiency made it reasonable to assume that tomorrow’s hardware would simply run today’s models faster. Engineers could design algorithms largely independent of underlying hardware constraints, relying on linear performance improvements to absorb the complexity of badly designed algorithms. That assumption no longer holds. Modern computing is entering a regime defined less by raw speed and more by combinatorial structure, architectural diversity, and hard constraints on energy, memory, and parallelism.
In digital twins, this shift becomes concrete in several ways. Models increasingly require hardware-aware co-design, aligning algorithms with GPU parallelism, vectorized execution, and memory locality. Hybrid computational stacks combine physics-based solvers, optimization routines, and learned neural surrogates (usually neural networks that approximate the behavior of more expensive, physics-based or algorithmic models, but run much faster), each mapped to different hardware tiers.
Compute-aware modeling treats fidelity and resolution as adaptive choices rather than fixed parameters, while approximate inference replaces exact solutions with bounded, tractable approximations suitable for real-time operation. As a result, mathematical modeling is now inseparable from computational feasibility. Exhaustive computation was never truly practical; decades of hardware improvement merely postponed its consequences by masking poor algorithmic scaling. As gains from added compute diminish and architectural constraints dominate, digital twins must rely on representations that scale gracefully—preserving useful insight even when hardware can no longer compensate for computational inefficiency and poor design. The illusion of hardware improvements that Moore’s law provided for decades is now gone.
Come the era of quantum compute and model-system-compute co-design.
#newbook #math #computation #digitaltwins #enterprisemodeling #mooreslaw
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