---
kind: concept
slug: informed-machine-learning
title: Informed machine learning
summary: >-
  Training a model on data plus explicit prior knowledge, such as equations, logic rules, simulator output, invariances or human feedback. The knowledge can enter through the training data, the hypothesis set, the learning algorithm or the final hypothesis. One survey card so far, with no experiments of its own; it gives a taxonomy, not measured results.
tags: [prior-knowledge, hybrid-learning, taxonomy, survey]
papers: ["1903.12394"]
related: [physics-informed-neural-network, neural-symbolic-integration, constrained-conditional-models, commonsense-knowledge-injection, equivariance-constraint]
status: draft
updated_at: 2026-10-19
---

## Overview

Informed machine learning means learning from data together with prior
knowledge that exists apart from the learning task and is written in a formal
form [arxiv:1903.12394 §2.2] [arxiv:1903.12394 §2.2.2]. The knowledge can be a
physical equation, a logic rule, the output of a simulator, an invariance, a
knowledge graph, a probability relation or a person's feedback
[arxiv:1903.12394 §4.2].

The motivation is that data alone can fall short when data is scarce, when a
model must obey natural laws or safety rules, or when a result has to be
explainable [arxiv:1903.12394 §1]. The survey gives one shared vocabulary for
these methods, the taxonomy below, which covers the whole pipeline rather than
one technique [arxiv:1903.12394 §2] (card: [Informed Machine Learning: A Taxonomy and Survey](/papers/1903.12394)).

Related names for overlapping work include physics-informed deep learning,
physics-guided neural networks and semantic-based regularisation
[arxiv:1903.12394 §1]. See [physics-informed neural networks](/concepts/physics-informed-neural-network)
for the most common physics case.

## Taxonomy

Each method can be placed on three axes [arxiv:1903.12394 §4]:

1. **Knowledge source.** Scientific, world or expert knowledge. The list is
   "neither complete nor disjoint", so one source may fall into several
   categories [arxiv:1903.12394 §4.1].
2. **Knowledge representation.** Eight forms, from equations and simulation
   results to logic rules, graphs, symmetries, probability assumptions and
   human input [arxiv:1903.12394 §4.2].
3. **Integration point.** Where the knowledge enters the pipeline: the training
   data, the hypothesis set, the learning algorithm, or the final hypothesis
   [arxiv:1903.12394 §4.3].

## Variants

Variants are grouped by integration point. A method can use more than one.

### Through the training data

Knowledge is turned into extra labelled or unlabelled samples, most often
simulation results [arxiv:1903.12394 §3.2.3]. The survey lists this as the
usual route when the goal is to need less real data [arxiv:1903.12394 §3.2.3].
It also says that data augmentation with virtual examples is mathematically
equivalent to a regulariser, citing the source for this claim without deriving
it [arxiv:1903.12394 §5.4]. Simulated data can differ from real data, and the
survey names adversarial domain adaptation and domain randomisation as
directions, without measured effects [arxiv:1903.12394 §5.3] [arxiv:1903.12394 §7].

### Through the hypothesis set (architecture)

The structure of the model encodes the knowledge. Knowledge graphs, spatial
invariances and logic rules often enter here [arxiv:1903.12394 §3.2.3]. The
clearest example is KBANN, which builds a network from propositional rules and
then refines its weights by learning [arxiv:1903.12394 §5.5]. The survey lists
whether this approach works for deep networks as an open question
[arxiv:1903.12394 §7].

### Through the learning algorithm (loss)

Knowledge becomes an extra term in the training objective. Equations, logic
rules, probability relations and human feedback most often change the algorithm
this way [arxiv:1903.12394 §3.2.3]. The example in the text is a knowledge
term that penalises violations of the given equations, with weights on the
label, regulariser and knowledge terms [arxiv:1903.12394 eq. 1]
[arxiv:1903.12394 §5.1]. The knowledge term needs only inputs and the model,
not labels [arxiv:1903.12394 §5.1]. The loss term is the form used by
[physics-informed neural networks](/concepts/physics-informed-neural-network).

Logic rules must become differentiable to be used in this way. The survey
mentions relaxing them "for example via the t-norm" but does not pick one
[arxiv:1903.12394 §5.5].

### Through the final hypothesis

The model's output is checked or corrected against the knowledge. The survey
classes this as aiming at knowledge conformity [arxiv:1903.12394 §3.2.3]. The
survey gives no method details for this route beyond the classification.

## When to use which

The survey does not benchmark the methods. The table maps a constraint to the
integration point that the surveyed literature uses for it. It does not rank
the options.

| Situation | Use | Why |
|---|---|---|
| A simulator exists and real data is scarce | Training data | Simulation results most often enter the training data, and this route aims at needing less data [arxiv:1903.12394 §3.2.3] |
| Known equations describe the system | Loss term | Scientific knowledge is mostly equations and simulation results; equations most often change the learning algorithm [arxiv:1903.12394 §3.2.2] [arxiv:1903.12394 §3.2.3] [arxiv:1903.12394 §5.1] |
| Domain rules are logical and the model should follow their structure | Hypothesis set (e.g. KBANN) | Logic rules and invariances often enter the hypothesis set [arxiv:1903.12394 §3.2.3]; KBANN is the example [arxiv:1903.12394 §5.5]; its use in deep networks is open [arxiv:1903.12394 §7] |
| Outputs must conform to rules | Final hypothesis | The stated aim of this route is conformity [arxiv:1903.12394 §3.2.3] |
| Knowledge is expert judgement without formal equations | Loss term with human feedback | Expert knowledge is mostly probabilistic relations or human feedback [arxiv:1903.12394 §3.2.2] |
| Interpretability is the main goal | Do not rely on this survey | In the classified papers, interpretability is only a minor goal [arxiv:1903.12394 §7] |

Note that most papers in the survey aim at better performance [arxiv:1903.12394 §3.2.3].

## Implementation sketch

Common core: a single objective that adds a knowledge term to the usual label
loss and regulariser [arxiv:1903.12394 eq. 1]. The variants differ in what
the knowledge term measures, and where the knowledge enters if it is not a
loss term.

```pseudocode
# Objective with a knowledge term  [arxiv:1903.12394 eq. 1] [§5.1]
# Input:  model f, labelled pairs (x_i, y_i), weights lam_l, lam_r, lam_k
# Output: scalar objective to minimise

def informed_objective(f, xs, ys, lam_l, lam_r, lam_k):
    # Label term: usual loss over the labelled samples  [eq. 1]
    label_term = sum(loss(f(x), y) for x, y in zip(xs, ys))
    # Regulariser R(f) on the model  [eq. 1]
    reg_term = regulariser(f)
    # Knowledge term: penalises violations of the given equations  [§5.1]
    knowledge_term = knowledge_loss(f, xs)
    return lam_l * label_term + lam_r * reg_term + lam_k * knowledge_term
```

The survey does not set the form of `knowledge_loss` or the values of the
weights. It names the weighting as a challenge [arxiv:1903.12394 §7].

## Contradictions

None known. The survey reports no experiments, so no numbers conflict. Names
for overlapping methods vary [arxiv:1903.12394 §1], which can make results hard
to compare.

## Open problems

- **Weights.** How to balance knowledge against labels is open [arxiv:1903.12394 §7].
- **Rule learning.** How to learn rules when none are given is open [arxiv:1903.12394 §7].
- **Evaluation.** Knowledge graphs are often customised per paper, so comparing
  them is hard [arxiv:1903.12394 §7].
- **Coverage.** The survey does not list its sources, search terms or date range,
  and says it does not claim to cover all research [arxiv:1903.12394 §1]
  [arxiv:1903.12394 §3.1.2]. Treat its "main paths" as a sample, not a census.

## Papers

- [Informed Machine Learning: A Taxonomy and Survey of Integrating Knowledge into Learning Systems](/papers/1903.12394): the taxonomy (source, representation, integration point) and a survey of how prior knowledge is integrated.