---
id: "design-modern-lfm-kernel"
title: "Design modern LFM kernel architecture"
status: "Proposed"
priority: "High"
created: "2025-08-15"
last_updated: "2025-08-15"
owner: "Neil Lawrence"
github_issue: ""
dependencies: "lfm-kernel-code-review"
tags:
- lfm
- kernel
- design
- architecture
---

# Design modern LFM kernel architecture

## Description
Design a modern LFM kernel implementation that follows GPy's current architectural patterns and uses the multioutput kernel approach with output index as input.

## Background
- Current GPy LFM implementations don't use the modern multioutput kernel approach
- Need to design a unified LFM kernel that integrates well with GPy's current framework
- Should maintain backward compatibility while providing improved functionality

## Design Requirements
- [ ] Use GPy's multioutput kernel approach with output index as input
- [ ] Follow consistent API design with other GPy kernels
- [ ] Implement proper parameter handling and constraints
- [ ] Support different base kernels for latent functions
- [ ] Enable efficient gradient computation
- [ ] Maintain backward compatibility with existing implementations

## Design Tasks
- [ ] Define kernel class structure and inheritance hierarchy
- [ ] Design parameter handling for mass, damper, spring, sensitivity, delay
- [ ] Plan integration with GPy's multioutput framework
- [ ] Design cross-kernel computation methods
- [ ] Plan parameter tying and constraint handling
- [ ] Design efficient computation methods for large datasets

## Acceptance Criteria
- [ ] Complete design specification document
- [ ] API design that follows GPy patterns
- [ ] Integration plan with existing GPy infrastructure
- [ ] Performance considerations documented
- [ ] Backward compatibility strategy defined

## Implementation Notes
- Study how other multioutput kernels in GPy handle output indices
- Consider parameter tying approaches from MATLAB implementation
- Design for extensibility to different differential equation types
- Plan for efficient computation of cross-kernel terms

## Related
- CIP: 0001 (LFM kernel implementation)
- Backlog: lfm-kernel-code-review