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Neural Networks

Operations

An Example

Current tools available

• OpenSees: build a map Φ : P → U

New Questions

• What does X - space look like?

Requirements for Composition

• Define an operation as a primitive that is closed under

  • Linear Algebra
  • Differentiation

• Stage computations

Purpose

• Explore/demonstrate the utility of a neural-like framework for structural modeling

Core Data Types

• anabel.Operation
• anabel.Assembler
• anabel.Template

anabel.Operation

Requires:

• shape
• parameters (ElemData schema)
• origin (ElemState)

Optional:

• tangents

Core API

• bind: Create an operation by binding a function to the input of an operation

Frame Template

@anabel.template(3)
def beam2d_template(
    q0: array = None,
    E:  float = None,
    A:  float = None,
    I:  float = None,
    L:  float = None
):
    def beam(v, q, state=None, E=E,A=A,I=I,L=L):
        C0 = E*I/L
        C1 = 4.0*C0
        C2 = 2.0*C0
        k = anp.array([[E*A/L,0.0,0.0],[0.0,C1,C2],[0.0,C2,C1]])
        return v, k@v, state
    return locals()

Parameterization

A = b_ft_f + b_wt_w

Structural Composition

import anabel

model = anabel.SkeletalModel(ndm=2, ndf=3)

bw, tw = 18, 18
tf, bf = model.param("tf","bf")
# define an expression for the area
area = lambda tf, bf: bf*tf + bw*tw
# create a model parameter from this expression
A  = model.expr(area, tf, bf)
...
# instantiate a `beam` in terms of this expression
girder = beam_template(A=A, I=I, E=3600.0)

Model Composition

Results