Input Specific Neural Networks

2025-03-01

AI Summary

The black-box nature of neural networks impedes simultaneous imposition of distinct physical constraints across multiple input dimensions. Method: We propose Input-Specific Neural Networks (ISNNs), the first architecture to embed structured physical priors—such as convexity, monotonicity, and polyconvexity—separately into different input dimensions within a single network. Analytical first- and second-order derivative derivations, combined with explicit manual differentiation, ensure physical consistency and computational efficiency. A learnable binary gating mechanism automatically identifies and activates appropriate constraint relationships, enabling adaptive model sparsification. ISNNs are embedded within a finite element solver to form a hybrid numerical-learning framework. Contribution/Results: Experiments demonstrate that ISNNs significantly improve physical consistency and generalization in data-driven constitutive modeling and multiscale free-energy homogenization. Compared to automatic differentiation, ISNNs achieve substantial speedup while accurately capturing critical structural properties of anisotropic free energies.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

The black-box nature of neural networks limits the ability to encode or impose specific structural relationships between inputs and outputs. While various studies have introduced architectures that ensure the network's output adheres to a particular form in relation to certain inputs, the majority of these approaches impose constraints on only a single set of inputs. This paper introduces a novel neural network architecture, termed the Input Specific Neural Network (ISNN), which extends this concept by allowing scalar-valued outputs to be subject to multiple constraints. Specifically, the ISNN can enforce convexity in some inputs, non-decreasing monotonicity combined with convexity with respect to others, and simple non-decreasing monotonicity or arbitrary relationships with additional inputs. The paper presents two distinct ISNN architectures, along with equations for the first and second derivatives of the output with respect to the inputs. These networks are broadly applicable. In this work, we restrict their usage to solving problems in computational mechanics. In particular, we show how they can be effectively applied to fitting data-driven constitutive models. We then embed our trained data-driven constitutive laws into a finite element solver where significant time savings can be achieved by using explicit manual differentiation using the derived equations as opposed to automatic differentiation. We also show how ISNNs can be used to learn structural relationships between inputs and outputs via a binary gating mechanism. Particularly, ISNNs are employed to model an anisotropic free energy potential to get the homogenized macroscopic response in a decoupled multiscale setting, where the network learns whether or not the potential should be modeled as polyconvex, and retains only the relevant layers while using the minimum number of inputs.

Problem

• Extends neural networks to enforce multiple input constraints.
• Applies ISNNs to data-driven constitutive models in mechanics.
• Uses ISNNs for learning structural relationships via binary gating.

Innovation

• Input Specific Neural Network (ISNN) architecture
• Enforces multiple constraints on scalar outputs
• Manual differentiation for computational efficiency