Neural Network Conservation Law Discovery via Contrastive Learning

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Solution Overview

Problem

Existing methods for automatic discovery of scientific laws, such as symbolic regression, rely on human knowledge and are computationally expensive, limiting their scalability and applicability to small physics equations.

Innovation Solution

A neural network-based approach using contrastive learning to automatically capture system invariants from data, employing a neural projection layer to ensure that the learned dynamics models preserve these invariants.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Extent of automation

If symbolic regression is used to automatically discover conservation laws, then automation of scientific law discovery is improved, but computational cost increases significantly

Engineering Contradiction:

Improveautomation of conservation law discoveryVSAvoidcomputational cost

Core Design Contradiction:

Extent of automationVSUse of energy by moving object

Solution Approach 1:

The patent replaces the mechanical/computational search process of symbolic regression with a neural network-based approach. The neural network learns conservation laws from data through contrastive learning, substituting the computationally intensive symbolic manipulation with a data-driven neural network training process that is more scalable and less resource-intensive for complex systems.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The neural network performs self-learning of conservation laws from trajectory data without requiring external guidance or human input. The contrastive learning mechanism allows the network to automatically discover invariants by comparing similar and dissimilar states, enabling autonomous scientific law discovery without the need for predefined function classes or manual feature engineering.

Inventive Principle:

Principle #25Self-service

2Extent of automation

If symbolic regression is used to discover conservation laws, then automatic discovery capability is improved, but scalability to complex systems deteriorates

Engineering Contradiction:

Improveautomatic discovery capabilityVSAvoidscalability to complex systems

Core Design Contradiction:

Extent of automationVSAdaptability or versatility

Solution Approach 1:

The neural network framework provides a universal approach that can handle various types of physical systems with different conservation laws. The same contrastive learning mechanism works across different domains (mechanical, electromagnetic, thermal systems), making the method universally applicable to complex systems without requiring system-specific customization or manual intervention.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent changes the fundamental parameters of the approach by using neural network representations instead of symbolic math expressions. This parameter change enables the system to scale to complex dynamics by leveraging the network's ability to learn high-dimensional patterns and non-linear relationships, overcoming the limitations of symbolic regression in handling complicated systems.

Inventive Principle:

Principle #35Parameter changes

3Adaptability or versatility

If conventional neural networks are used for dynamics modeling, then modeling flexibility is improved, but trustworthiness and conservation property preservation deteriorate

Engineering Contradiction:

Improvemodeling flexibilityVSAvoidtrustworthiness and conservation preservation

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent introduces feedback mechanisms through contrastive learning that continuously monitor and adjust the neural network's predictions. The network receives feedback from comparing predicted trajectories with actual conserved quantities, allowing it to learn and correct violations of conservation laws. This feedback loop ensures the model maintains both flexibility and trustworthiness by aligning predictions with physical principles.

Inventive Principle:

Principle #23Feedback

Solution Approach 2:

The neural network performs preliminary learning of conservation laws from trajectory data before being used for dynamics modeling. By pre-training on conserved quantities and using contrastive learning to establish the relationship between states and invariants, the network is prepared to naturally preserve conservation properties during subsequent prediction tasks, ensuring reliability without sacrificing modeling flexibility.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS20250028973A1Neural network-based dynamical system modeling for contrastively learned conservation laws

Publication Date: 2025.01.23 INTERNATIONAL BUSINESS MACHINE CORPORATION

AI summary

Obtain, using at least one hardware processor, data characterizing a physical system governed by a physical conservation law. Apply, using the at least one hardware processor, contrastive learning to the data to automatically capture system invariants of the physical system. Employ, using the at least one hardware processor, a neural projection layer to guarantee that a corresponding dynamic machine learning model preserves the captured system invariants. Optionally, predict performance of the physical system using the corresponding dynamic machine learning model.