FROM LEARNING TO INFERENCE

What does the network do after training?

LEARNED READOUT FROZEN · DYNAMICS STILL RUN

1 · New input2 · Mechanical propagation3 · Local neural feedback4 · Learned output
Trained network inference through a continuous mediumA Warren truss bridge inspired by the supplied reference image has a single layer of 200 deck cells, two side trusses, spring supports at both ends and two interior pinned supports. Elevated neuron markers return local feedback. A live plot compares the learned readout, an untrained baseline and a reference target. Click or use the number control to inspect a cell. Projection shows in-plane motion, not out-of-plane bending. 01 / INPUT → COUPLED MEDIUM → READOUTWarren truss bridge · 200 deck cells · motion magnified · schematic geometryTeal → positive activation · violet → negative · gold outline → selected cell INSIDE THE TRAINED MODELParameters: held fixedDisplacement / velocity: evolveFull plastic model: internalmaterial state can also evolve.No optimizer during inference. 02 / DOES THE LEARNED OUTPUT FOLLOW THE TASK?Rolling 24 seconds · actual reduced-model trajectories · all signals normalized
– – Reference target━━ Trained readout━━ Untrained readoutBlue steel trusses · green supports · click a deck cell to inspect

Bridge-scale interpretation

The visual now follows your Warren truss bridge reference: 306.92 m overall length, spring supports at the ends, and two interior pinned supports. The 200 neuro cells are mapped to a schematic deck mesh; the blue truss members carry the structural form. Support spacing and member dimensions are illustrative.

A bridge DPCNN would couple deck and truss finite elements to neural feedback and use loads, temperature and support properties as model inputs. This animation keeps the existing reduced teaching dynamics; the drawn steel members and supports do not enter a calibrated bridge FE analysis.

HELD-OUT TEST · TOY MODEL
Evaluating…

Fixed test sequence, independent of the training input.

WHAT CHANGED IN TRAINING?

Here: only the output readout coefficients are fitted by ridge regression. The 200-cell dynamics and local tanh feedback are fixed. This is an executable teaching model, not a reproduction of either paper’s training algorithm.

NEW INPUT, SAME PARAMETERS

The response changes because the input and dynamical states change. Learning resumes only when an optimizer is explicitly enabled.

Training: minimize Σ ||ŷ(t; θ) − y_target(t)||² + regularization, subject to dynamics.
Inference: fix θ = θ*; integrate M ü + C u̇ + f_int(u, internal state; θ*) = f_input + f_neural.

NONLINEAR SYSTEM IDENTIFICATION

Learn a time-dependent input–output relation from paired excitation and measured response. Test on held-out histories before using the learned model for prediction. This is the application illustrated by the live target-following task.

PROPOSED BRIDGE EXTENSION

Use measured loads and responses to train a bridge-specific forward response model. Damage inference needs a separate inverse formulation, temperature and support variables, multiple sensors, and identifiability checks. Speedup requires reduction or a separate surrogate.

What exactly is computed here, and what would full DPCNN training require?

The demo integrates 200 coupled scalar oscillators with nearest-neighbor coupling, damping, a cubic restoring force, and local tanh force feedback using a fixed 0.04 time step. This normalized lattice has no finite-element shape functions, stress integration, or constitutive plasticity. Elevated neuron markers show local deck connections; they do not represent an extra material layer. The bridge has two Warren side trusses, top cross-bracing and schematic support symbols, inspired by the user-provided reference image. Its 306.92 m label is taken from that image; no dimensional bridge model or truss/support stiffness is solved. Skin and plate tabs explain different architectures; both use this same reduced teaching solver.

The target is an independent nonlinear damped oscillator driven by the same input. A linear readout of 36 displacement, velocity and nonlinear-activation features plus a bias is fitted on 2,200 samples of one multisine history after a 600-step warm-up. Validation uses a different multisine history, resets the dynamical state, discards its own warm-up and never refits the coefficients. Reported error is RMS prediction error divided by RMS reference response, without mean subtraction. Training amplitude is 1.0; other amplitudes are unvalidated.

For the research model, define the excitation histories, target output and loss first. Optimize the permitted synaptic weights and material variables through sensitivity analysis or another appropriate constrained optimizer. Enforce physical bounds and dynamic stability; use held-out loads and initial states. Save learned parameters together with the constitutive law and state-initialization procedure. Frozen parameters do not imply frozen plastic strain or hardening state.

Neuro-Skins: Joghataie & Shafiei Dizaji, 2019 studies dynamics, neuron types and cell size; training is outside that paper’s scope. Neuroplasticity: Joghataie & Shafiei Dizaji, 2016 develops a learning algorithm with adaptive base-material properties. The 200-neuron layout shown here is an illustrative extension of the plate study.

DPCNN = Dynamic Plastic Continuous Neural Network (the spelling used in the paper; sometimes typed DCPNN). This interactive experiment demonstrates inference concepts and readout fitting only. It reports no published DPCNN accuracy, hardware implementation, bridge validation, or real-time performance.