Satellite Effect Scheduling via Reverse Time Heat Isomorphism

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Solution Overview

Problem

Current methods for scheduling and delivering satellite effects are inefficient, relying on incremental advancements and iterative techniques that waste time and resources, especially when trying to achieve timely and optimal satellite behaviors.

Innovation Solution

The implementation of a communications apparatus that uses a reverse time heat equation isomorphism to optimize the delivery of satellite effects by constructing a generalized heat equation, separating variables, solving equations, applying boundary conditions, filtering solutions, and generating an optimized schedule based on formal differences.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If incremental advancements and iterative techniques are used for scheduling satellite effects, then the system can achieve satellite behavior fulfillment, but the time and resources required increase significantly

Engineering Contradiction:

Improvesatellite behavior fulfillmentVSAvoidtime for scheduling and delivery

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent applies inverse problems methodology by formulating the satellite scheduling problem as an inverse heat equation. Instead of iteratively adjusting parameters forward in time, the system works backward from the desired final state to determine optimal initial conditions and timing, effectively inverting the conventional iterative approach to achieve direct optimization of satellite effect delivery.

Inventive Principle:

Principle #13The other way round (Inversion)

Solution Approach 2:

The patent transforms the scheduling problem into a mathematical formulation involving parameter changes through the heat equation. By converting temporal and spatial parameters into a generalized heat equation framework with variables representing time, space, and satellite effects, the system enables analytical solutions that directly optimize delivery parameters without iterative adjustment.

Inventive Principle:

Principle #35Parameter changes

2Adaptability or versatility

If iterative techniques are used to achieve timely satellite behaviors, then the system can adjust to requirements, but computational resources and time are wasted

Engineering Contradiction:

Improveadjustment to requirementsVSAvoidcomputational efficiency

Core Design Contradiction:

Adaptability or versatilityVSProductivity

Solution Approach 1:

The patent replaces computational iterative optimization mechanisms with a mathematical analytical framework. By substituting numerical iteration with a closed-form solution to the inverse heat equation, the system achieves adaptability to varying requirements through mathematical parameter adjustment rather than computationally intensive iterative processes, significantly improving productivity.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Ease of manufacture

If conventional scheduling methods are used, then the system operates with existing constraints, but optimal delivery of satellite effects cannot be achieved

Engineering Contradiction:

Improvesystem operation simplicityVSAvoiddelivery optimization

Core Design Contradiction:

Ease of manufactureVSManufacturing precision

Solution Approach 1:

The patent creates a universal mathematical framework that handles multiple scheduling scenarios and constraints within a single generalized heat equation formulation. This multi-functional approach allows the system to address diverse satellite effect delivery requirements using the same mathematical tools, achieving optimal delivery precision while maintaining operational simplicity through unified methodology.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS20250171164A1Device for optimal satellite effects delivery via reverse time heat isomorphism

Publication Date: 2025.05.29 RAYTHEON CO

AI summary

Apparatus, computer-readable medium, and method for optimal delivery of one or more satellite effects via reverse time heat equation isomorphism including constructing a generalized formulation of the heat equation corresponding to a commander's intent for delivery of the one or more satellite effects, performing a separation of variables to decouple a plurality of variables into a plurality of corresponding separated equations, solving the plurality of separated equations to produce candidate solutions, applying boundary conditions to each candidate solution, filtering the candidate solutions to mitigate ill-posedness of solving the inverse of the heat equation, assessing formal differences between the candidate solutions and the inverse of the heat equation, and generating an optimized schedule of the one or more satellite effects based on the assessment of the formal differences of the candidate solutions.