Does a physical neural network have to be analog?

The term commonly highlights direct physical transformations, but implementations and surrounding systems can mix analog and digital components.

Can it use backpropagation?

Some approaches do, including hybrid methods that estimate gradients with a digital model.

Is every physical network energy-efficient?

No. Efficiency is an empirical whole-system claim, not a consequence of the name.

AI Glossary / Deep learning / Advanced

Physical neural network

Definition

A physical neural network uses controllable physical processes to carry out neural computation. Rather than representing every operation as conventional digital arithmetic, it can exploit electrical, optical, mechanical or other physical transformations as part of the learned system.

What it means

Every computer is physically built, so the phrase needs a more specific meaning. In this research context, the physical behavior is deliberately used as the computational operation: currents sum, waves interfere or a dynamical system transforms an input signal.

Usage varies. Some work maps familiar neural calculations onto specialized hardware, such as conductance arrays. Other work trains a physical transformation without requiring it to match a standard neural layer operation by operation. The implementation and the trainable quantities should therefore be stated explicitly.

A physical neural network is different from a physics-informed neural network. The former concerns how computation is performed. The latter incorporates physical knowledge into a learning problem and can run entirely on conventional electronic computers.

How it works

Inputs are encoded into physical signals, such as voltages or optical fields. Adjustable parameters control the system's response. A measurement converts that response into an intermediate representation or final output.

In a conductance crossbar, suitable applied voltages and device conductances can produce currents corresponding to a matrix-vector calculation. Real devices depart from an ideal mathematical array through effects such as variability and wire resistance.

Other architectures directly train physical transformations. Wright and colleagues demonstrated a physics-aware training approach combining a physical forward pass with gradients obtained using a differentiable digital model. Their experiments included mechanical, electronic and optical systems.

Training can occur before hardware programming, partly in the device, or through a hybrid procedure. A physical inference stage does not imply that training is entirely physical. Input preparation, parameter control, nonlinearities and readout may still require electronic or digital components.

Three practical examples

A research array represents numerical weights using adjustable conductances and evaluates an analog weighted sum.
An optical prototype transforms encoded inputs through a programmed light-processing stage before an electronic readout.
A mechanical learning experiment uses a controllable vibrating structure as part of a trained input-output transformation.

Think of it this way

Think of shaping a channel so that flowing water performs a useful transformation on an incoming flow pattern. Once constructed and controlled, the channel's behavior does part of the work rather than a computer calculating every intermediate movement.

This is an analogy for using a physical process, not a claim that arbitrary water channels are neural networks. Inputs, adjustable parameters, outputs and a learning procedure must be defined. The surrounding apparatus and its resource costs still matter.

Worked example

A physical weighted sum

Consider an idealized teaching circuit with two input voltages, 0.1 V and 0.2 V. Their corresponding conductances into one summing output are 20 microsiemens and 30 microsiemens. Assuming ideal voltage application and current collection, the contributions are 2 microamperes and 6 microamperes, giving 8 microamperes in total.

The physical relations implement a weighted sum: voltage multiplied by conductance gives current, and the currents combine. If the second conductance is actually 27 microsiemens, the total becomes 2 + 5.4 = 7.4 microamperes, a 7.5% reduction from the ideal result.

This is not a complete neural classifier. It omits activation, signed-weight encoding, conversion and nonideal wiring. Its purpose is to show both the computational mapping and why physical parameter errors must be assessed in the complete task rather than ignored.

Illustrative case study

Fictional example: Willow Signal Systems evaluates an analog neural component for a repeatedly executed sensor calculation. A digital model predicts satisfactory accuracy using nominal component settings. Measurements from several physical units show small but systematic differences.

The team tests calibration and training procedures that account for the measured hardware response. It records which parameters are shared across units and which require device-specific adjustment. It then repeats evaluation after the expected operating conditions change.

The business comparison includes input conversion, readout, calibration time and the cost of updating the model. A promising computational core remains a research prototype until the whole pipeline meets the required accuracy and maintenance constraints.

The lesson is that learning can sometimes accommodate imperfections, but resilience must be demonstrated for the actual device and operating range. It cannot be assumed from the word physical.

Common misconceptions and mistakes

Physical means no software. Hybrid training, control and readout are common design choices.
A physical network must copy every biological detail. Useful hardware computation can be inspired by learning without being a biological replica.
Analog arithmetic has unlimited precision. Noise, variability and measurement limits affect usable precision.
Physics-informed and physical neural networks are interchangeable. They describe different aspects of a system.

Business use

The potential value lies in matching a workload to a physical process that performs useful transformations efficiently. This is especially relevant when investigating specialized accelerators or computing near a sensor.

Request complete-system evidence: accuracy on representative inputs, throughput, energy, calibration requirements, parameter-update costs and device variability. Separate simulation results from measured hardware results. Also establish whether a model change requires software, reprogramming or new fabrication. An advantage for one fixed transformation may not transfer to rapidly changing, general-purpose workloads.

Check your understanding

A prototype performs inference in a physical device but computes training gradients on a conventional computer. Is it accurate to say all learning occurs physically?

Answer: No. Describe the hybrid procedure: the physical device performs the relevant forward transformation while digital computation supports training.

Related terms

Optical neural network
Physics-informed neural networks
Analog computing
memristor
neuromorphic computing
hardware accelerator
physics-informed neural network
in-memory computing

Learn next

Read analog computing and physics-informed neural network. Draw a proposed physical system's input encoding, adjustable parameters and readout, then identify which stages are measured hardware and which are simulated or digital.

Neural network

Sources

Wright et al., Deep physical neural networks trained with backpropagation: https://www.nature.com/articles/s41586-021-04223-6. Authors' instructional implementation: https://github.com/mcmahon-lab/Physics-Aware-Training. Experimental conductance-array learning: https://www.nature.com/articles/s41467-018-04484-2. Analog crossbar demonstration: https://www.nature.com/articles/s41467-021-25455-0. Circuit figures and the company case are original illustrations.

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