# AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledge
**Authors**: You-Le Fang, Dong-Shan Jian, Xiang Li, Yan-Qing Ma
> School of Physics, Peking University, Beijing 100871, China
> School of Physics, Peking University, Beijing 100871, China Center for High Energy Physics, Peking University, Beijing 100871, China
(December 11, 2025)
## Abstract
While current AI-driven methods excel at deriving empirical models from individual experiments, a significant challenge remains in uncovering the common fundamental physics that underlie these models—a task at which human physicists are adept. To bridge this gap, we introduce AI-Newton, a novel framework for concept-driven scientific discovery. Our system autonomously derives general physical laws directly from raw, multi-experiment data, operating without supervision or prior physical knowledge. Its core innovations are twofold: (1) proposing interpretable physical concepts to construct laws, and (2) progressively generalizing these laws to broader domains. Applied to a large, noisy dataset of mechanics experiments, AI-Newton successfully rediscovers foundational and universal laws, such as Newton’s second law, the conservation of energy, and the universal gravitation. This work represents a significant advance toward autonomous, human-like scientific discovery.
Introduction. — For centuries, the ultimate goal of fundamental physics research has been to describe a wide range of phenomena through a small number of discovered laws. Advances in artificial intelligence (AI) have made AI-driven scientific discovery a highly promising new paradigm [1]. Although AI has achieved remarkable results in tackling domain-specific challenges [2, 3], the ultimate aspiration from a paradigm-shifting perspective still lies in developing reliable AI systems capable of autonomous scientific discovery directly from a large collection of raw data without supervision [4, 5].
Current approaches to automated physics discovery focus on individual experiments, employing either neural network (NN)-based methods [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25] or symbolic techniques [26, 27, 28, 29, 30, 31, 32, 33]. By analyzing data from a single experiment, these methods can construct a specific model capable of predicting future data from the same experiment; if sufficiently simple, such a model may even be expressed in symbolic form [34, 35, 36]. Although these methods represent a crucial and successful stage towards automated scientific discovery, they have not yet reached a discovery capacity comparable to that of human physicists.
Human scientists advance further by discerning common patterns across specific models from different experiments and, on that basis, formulating general models that account for data from all such experiments. For instance, Newtonian mechanics provides a unifying and interpretable framework by defining meaningful physical concepts and formulating general laws that are valid across diverse phenomena. Therefore, a central challenge for the AI-driven physics discovery field is to evolve beyond problem-specific model fitting towards AI systems capable of discovering knowledge that is inherently generalizable and universally applicable.
In this Letter, we present AI-Newton, a concept-driven discovery system, which is designed for the critical question: how to extract concepts and general laws from problem-specific models. AI-Newton integrates an autonomous discovery workflow which is fundamentally built upon plausible reasoning and physical concepts. Given a collection of physical experiments, AI-Newton can gradually formulate a set of general laws applicable across a wide problem scope with neither supervision nor any prior physical knowledge. As a proof-of-concept implementation Code available at https://github.com/Science-Discovery/AI-Newton, by applying it to 46 different classical mechanics experiments, it can rediscover Newton’s second law, energy conservation, law of gravitation and others in classical mechanics.
<details>
<summary>overview.png Details</summary>
### Visual Description
## Diagram: Autonomous Discovery Workflow
### Overview
The image presents a conceptual framework for an "Autonomous discovery workflow." It is organized into three distinct vertical columns representing the flow of information from experimental data to theoretical knowledge. The diagram illustrates a closed-loop system where experimental data is processed through an automated workflow to generate or refine theoretical concepts and laws, which in turn inform the discovery process.
### Components/Axes
The diagram is divided into three main regions:
1. **Left Column (Green Background): "Experiment base"**
* Contains a stack of experiment blocks (Experiment 1, Experiment 2, ..., Experiment N).
* **Experiment 1** is detailed with the following sub-labels: "Physical objects", "Geometric information", "Experimental parameters", "Space-time coordinates", "Data generator".
2. **Center Column (Purple Background): "Autonomous discovery workflow"**
* Contains four stacked processing blocks, each enclosed in a distinct dashed border.
* **Top (Yellow dashed border):** "Selection" (contains "One experiment", "A few concepts").
* **Upper-Middle (Grey dashed border):** "Search of physical laws" (contains "Extension of general laws", "Direct search of specific laws").
* **Lower-Middle (Red dashed border):** "Simplification and classification".
* **Bottom (Blue dashed border):** "Extraction of concepts and general laws".
3. **Right Column (Blue Background): "Theory base"**
* Contains three stacked blocks representing theoretical hierarchy:
* **Top:** "Symbols".
* **Middle:** "Concepts" (contains "Dynamical concepts", "Intrinsic concepts", "Universal constants").
* **Bottom:** "Laws" (contains "Specific laws", "General laws").
* Bi-directional arrows connect "Symbols" to "Concepts" and "Concepts" to "Laws," labeled "represent" (downward) and "extract" (upward).
**Legend (Bottom):**
The legend maps the dashed borders in the center column to specific methodologies:
* **Yellow dashed box:** Recommendation engine
* **Grey dashed box:** Symbolic regression
* **Red dashed box:** Differential algebra & variable control
* **Blue dashed box:** Plausible reasoning
### Detailed Analysis
**Flow and Connectivity:**
* **Input:** An arrow labeled "Experiments" points from the "Experiment base" (Left) to the "Autonomous discovery workflow" (Center).
* **Internal Workflow:** Vertical arrows connect the four blocks in the center column, indicating a sequential process: Selection $\rightarrow$ Search of physical laws $\rightarrow$ Simplification and classification $\rightarrow$ Extraction of concepts and general laws.
* **Feedback/Interaction:** Two-way arrows labeled "Concepts" and "Laws" connect the "Autonomous discovery workflow" (Center) to the "Theory base" (Right). This indicates that the workflow both utilizes existing concepts/laws and contributes new ones back to the theory base.
**Methodology Mapping:**
* **Selection:** Utilizes a **Recommendation engine** (Yellow).
* **Search of physical laws:** Utilizes **Symbolic regression** (Grey).
* **Simplification and classification:** Utilizes **Differential algebra & variable control** (Red).
* **Extraction of concepts and general laws:** Utilizes **Plausible reasoning** (Blue).
### Key Observations
* **Hierarchical Abstraction:** The "Theory base" is structured hierarchically, moving from abstract "Symbols" to "Concepts" and finally to "Laws." The bi-directional arrows suggest a continuous refinement process where symbols represent concepts, and concepts are extracted from laws, and vice versa.
* **Modular Workflow:** The center column breaks down the discovery process into four distinct computational tasks, each associated with a specific algorithmic approach (Recommendation, Regression, Algebra, Reasoning).
* **Data-Driven Loop:** The system is designed to ingest raw experimental data (left) and output structured theoretical knowledge (right), with the workflow acting as the bridge.
### Interpretation
This diagram depicts an **automated scientific discovery pipeline**, likely representing an AI-driven system designed to perform physics research.
* **The "Closed-Loop" Nature:** The interaction between the "Autonomous discovery workflow" and the "Theory base" suggests a system that does not just output static results but iteratively updates its own theoretical understanding. By extracting concepts and laws, the system improves its ability to perform future "Selection" and "Search" tasks.
* **Methodological Rigor:** The specific assignment of techniques (e.g., "Symbolic regression" for searching laws, "Differential algebra" for simplification) suggests a highly structured approach to AI-driven science. It implies that the system treats scientific discovery as a formal optimization and classification problem rather than a purely generative one.
* **Peircean Investigative Logic:** The flow mirrors the scientific method:
1. **Abduction (Selection):** Choosing which experiments to run based on current knowledge.
2. **Induction (Search/Simplification):** Finding patterns (laws) in the data.
3. **Deduction (Extraction):** Formalizing these patterns into concepts and laws that can be tested again.
* **Significance:** This architecture is characteristic of modern "AI for Science" (AI4Science) frameworks, which aim to accelerate scientific discovery by automating the transition from raw experimental observations to fundamental physical laws.
</details>
Figure 1: AI-Newton’s experiment base, theory base, and autonomous discovery workflow.
Knowledge base and knowledge representation. — AI-Newton contains an experiment base and a theory base, as shown in Fig. 1. The experiment base stores physical experiments and corresponding simulated data generators. The inputs for each experiment include only the physical objects involved, geometric information, experimental parameters, and space-time coordinates, which define an experiment. To emphasize that no prior physical knowledge is used, all other concepts, such as mass or energy, are autonomously discovered in AI-Newton. The output of each experiment is simulated data with statistical errors.
The theory base stores physical knowledge explicitly in an interconnected library of symbols, concepts, and laws. This design mirrors how human physicists construct concise, universal laws from conceptual building blocks. In contrast to prior work, which interprets latent features in NNs as physical concepts [37, 23, 38], AI-Newton represents concepts and laws in an explicit, symbolic form. This greatly enhances interpretability and makes the acquired knowledge easier to transfer to new problems. Moreover, the introduction of powerful intermediate concepts allows complex physical laws to be expressed concisely, which in turn makes them more amenable to discovery through techniques like symbolic regression (SR) [26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]. Initially, the concept layer contains only space-time coordinates; new concepts are autonomously defined and registered using a dedicated physical domain-specific language (DSL). (See Supplemental Materials (SMs) [39] for details.)
A robust knowledge representation is crucial because our goal is for the AI to discover generalizable knowledge across diverse systems, which requires transferring knowledge between different problems. To achieve this, we designed a physical DSL with a well-defined structure. This DSL not only formulates equations but also encodes the properties of physical objects and the relationships between physical quantities. For instance, given the known concepts of coordinate $x$ and time $t$ , the velocity of a ball can be defined in the DSL as:
$$
C_{1}:=\forall i\text{: Ball},\,\mathrm{d}x[i]/\mathrm{d}t, \tag{1}
$$
where $i$ indexes the balls and $C_{1}$ denotes the symbol of velocity, with the subscript $1$ varying across tests. In addition to dynamical concepts like velocity, the system also automatically identifies two other types: intrinsic concepts (e.g., mass, spring constant), which depend solely on specific physical objects, and universal constants (e.g., the gravitational constant), which are independent of all other quantities. Both are defined by documenting their measurement procedures. For example, mass of a ball could be defined as:
$$
\begin{split}C_{2}:=&\forall i\text{: Ball},\text{Intrinsic}[\\
&\text{ExpName}(o_{1}\rightarrow i,o_{2}\to s),\text{L}[s]-\text{L}_{0}[s]],\end{split} \tag{2}
$$
where ExpName is the name of an experiment. In this experiment, the measured ball $i$ is suspended from a fixed spring $s$ , and the spring elongation $\text{L}[s]-\text{L}_{0}[s]$ serves as the measurement of the mass. Recording the measurement procedures of intrinsic concepts is essential, since it allows the value of an intrinsic property to be retrieved by invoking its defining experiment, ensuring conceptual consistency across different problems.
These explicit concepts serve as the building blocks for the laws layer, which stores discovered physical laws, such as conserved quantities and dynamical equations. The laws are categorized into specific laws (valid for one experiment with specific forms) and general laws (valid across diverse experiments with general forms). Within this framework, prior research in AI-driven physics discovery has concentrated on identifying specific laws. The introduction of general laws enables AI-Newton to simultaneously describe physics in various complex systems with compact and concise formulations. For instance, consider a system with a ball on an inclined plane connected to a fixed end via a spring. By applying the general law discovered by AI-Newton (Newton’s second law in the $x$ -direction):
$$
\forall i:\text{Ball},\,m_{i}a_{i,x}+(\nabla_{i}V_{g})_{x}+(\nabla_{i}V_{k})_{x}=0, \tag{3}
$$
the more complex dynamical equation of the ball can be concretely derived as:
$$
\begin{split}&ma_{x}-\frac{c_{x}c_{z}}{c_{x}^{2}+c_{y}^{2}+c_{z}^{2}}mg\\
+&\frac{\left[\left(c_{y}^{2}+c_{z}^{2}\right)x-c_{x}\left(c_{y}y+c_{z}z\right)\right]}{\left(c_{x}^{2}+c_{y}^{2}+c_{z}^{2}\right)L}k\Delta{L}=0,\end{split} \tag{4}
$$
where $(c_{x},c_{y},c_{z})$ is the normal vector defining the inclined plane. For multi-object systems, concrete dynamical equations can be much more complex than the general laws, making them hard to be obtained using previous symbolic approaches. These cases highlight the efficacy of our concept-driven hierarchical approach.
Autonomous discovery workflow. — The autonomous discovery workflow in AI-Newton continuously distill knowledge—expressed as physical concepts and laws—from experimental data, as shown in Fig. 1. Plausible reasoning, a method based on rational inference from partial evidence [40, 41], is the key to discovering knowledge. Unlike deductive logic, it produces contextually reasonable rather than universally certain conclusions, mirroring scientific practice where hypotheses precede rigorous verification.
The workflow initiates each trial by selecting an experiment and a few concepts from the theory base. This selection is governed by a recommendation engine that integrates a UCB-inspired value function [42, 43, 44, 45, 46] with a dynamically adapted NN. The NN’s architecture is updated in real-time to favor configurations that lead to efficient knowledge extraction. This mechanism enables the system to emulate human-like learning, naturally balancing the trade-off between exploration and exploitation.
To ensure the workflow establishes foundational knowledge before tackling complex experiments, we introduce an era-control strategy. Within a given era, every trial must conclude within a specific wall-clock time limit. If no new knowledge is acquired after a sufficient number of trials, the system advances to a new era with an exponentially increased time limit. Consequently, this strategy keeps the system focused on simpler experiments in the early phases. (See SMs [39] for more details.)
The next step of each trial is to explore new laws from the selected experiment and concepts. Specific laws can be discovered through direct searching for relations among the selected concepts within the allowed operational space, which is nothing but SR. Our SR implementation combines direct instantiation-verification and PCA-based differential polynomial regression [47, 48, 49, 50]. Furthermore, new general laws may emerge by extending existing ones through plausible reasoning. The core idea of plausible reasoning here is that, if a general law holds across multiple experiments but fails in the current one, there is a possibility to derive a valid modified law by adding simple terms to the original formulation via SR. For instance, while kinetic energy conservation governs elastic collisions, it fails in spring systems. Through plausible reasoning, AI-Newton introduces additional terms (elastic potential) to restore conservation. Mirroring human research practice, the system heuristically leverages existing general laws and selected concepts to search for physical laws that explain new experimental data.
The aforementioned process may generate redundant knowledge causing an explosion in both the theory base and search space that severely hinders continuous discovery under limited resources. To address this, AI-Newton simplifies physical laws into minimal representations in each trial. For the example shown in this paper, we employ the Rosenfeld Gröbner algorithm [51, 52, 53, 54] from differential algebra to perform the simplification (See SMs [39] for more details). Furthermore, through controlled-variable analysis, AI-Newton numerically identifies the dependencies of relations on physical objects and experimental parameters, using these dependencies as the basis for classification.
After identifying new laws, AI-Newton extracts new concepts from the processed results through plausible reasoning: a conserved quantity in the current experiment suggests broader utility, triggering its extraction as a new concept. Similarly, it proposes new general laws from directly-searched specific laws that also hold in multiple other experiments. All accumulated knowledge are updated to the theory base.
<details>
<summary>test_cases.png Details</summary>
### Visual Description
## Diagram: Conceptual Framework of Physical Experiments and Laws
### Overview
The image presents a conceptual framework mapping physical objects to experimental schematics and their corresponding mathematical laws. It is organized into three vertical columns: "Physical objects" (left), "Schematic of experiments" (center), and "Discovered important general laws" (right). The diagram illustrates how simple physical components (spheres, springs, wedges) are combined into experimental setups (numbered 1-8) and how these setups are governed by specific energy conservation and motion equations.
### Components/Axes
**Column 1: Physical objects**
* **Top:** A single white sphere.
* **Middle:** A metallic helical spring.
* **Bottom:** A grey triangular wedge (inclined plane).
**Column 2: Schematic of experiments**
* **Region 1 (Top):**
* (1) A sphere moving right; a spring moving right.
* (2) Two spheres moving towards each other, then interacting, then moving away.
* **Region 2 (Middle):**
* (3) Three sub-diagrams showing chains of spheres connected by springs (1 spring/2 spheres, 2 springs/3 spheres, 3 springs/4 spheres).
* (4) Two sub-diagrams: a spring-sphere system oscillating, and a triangular configuration of three spheres connected by springs.
* **Region 3 (Bottom):**
* (5) "gravity near Earth's surface": Two spheres, one falling vertically, one bouncing.
* (6) A sphere rolling down an inclined plane.
* (7) A pendulum-like system of spheres and springs hanging from a horizontal surface.
* (8) A spring-sphere system resting on an inclined plane.
**Column 3: Discovered important general laws**
* **Header:** "Energy conservation"
* **Equation:** $\sum_{\kappa \in \{x,y,z\}} T_\kappa + \sum_{\lambda \in \{k,g,G\}} \delta_\lambda V_\lambda = \text{const.}$
* **Definitions:**
* $T_\kappa = \sum_{i \in \text{Particles}} m_i v_{i,\kappa}^2$
* $V_k = \sum_{i \in \text{Springs}} k_i (L_i - L_{0,i})^2$
* $V_g = \sum_{i \in \text{Particles}} 2 m_i g z_i$
* $V_G = \sum_{i,j \in \text{Particles}} 2 \left( -\frac{G m_i m_j}{r_{ij}} \right)$
* **Diagram (9):** "universal gravitation" showing interaction pairs (2 spheres), triplets (3 spheres), and quadruplets (4 spheres) connected by dotted lines with circular arrows indicating gravitational influence.
* **Header:** "Newton's second law"
* **Equation:** $2a_\kappa + \sum_{\lambda \in \{k,g,G\}} \delta_\lambda \left( \frac{1}{m} \frac{\partial V_\lambda}{\partial \kappa} \right) = 0, \quad \kappa \in \{x, y, z\}.$
* **Footer:** "($\delta_\lambda = 0$ or $1$, determined spontaneously during instantiation as specific laws in experiments)"
### Detailed Analysis
* **Energy Conservation Formulation:** The equation defines the total energy as the sum of kinetic energy ($T_\kappa$) and potential energies ($V_\lambda$). The index $\kappa$ represents spatial dimensions $\{x, y, z\}$, and $\lambda$ represents force types $\{k, g, G\}$ (spring, gravity, universal gravitation).
* **Mathematical Notation:**
* The kinetic energy term $T_\kappa$ uses $m_i v_{i,\kappa}^2$.
* The spring potential $V_k$ uses the standard Hooke's law form $k(L-L_0)^2$.
* The gravitational potential $V_g$ (near surface) uses $2 m_i g z_i$.
* The universal gravitation potential $V_G$ uses $2 (- \frac{G m_i m_j}{r_{ij}})$.
* **Newton's Second Law:** The equation is presented in a force-balance form: $2a_\kappa + \sum \dots = 0$. This implies that the acceleration $a_\kappa$ is directly related to the gradient of the potential energy terms.
* **The $\delta_\lambda$ Variable:** This is a binary switch (0 or 1). It acts as a selector. If a specific force (e.g., gravity) is not present in an experiment, $\delta_g$ becomes 0, effectively removing that term from the equation for that specific instance.
### Key Observations
* **Spontaneous Instantiation:** The note at the bottom is critical. It suggests that the system does not use a "one-size-fits-all" equation but rather "instantiates" the relevant laws based on the experimental setup.
* **Consistency:** The diagram (9) visually maps to the summation terms in $V_G$. The 2-sphere, 3-sphere, and 4-sphere configurations in diagram (9) correspond to the $i,j$ summation indices in the $V_G$ equation.
* **Notation Anomalies:** The equations include coefficients (like the '2' in $V_g$ and $V_G$, and the '2' in $2a_\kappa$) that are not standard in classical textbook physics (which usually use $1/2$ for kinetic/potential energy). This suggests this is a specific, perhaps custom, mathematical model or a representation of a machine-learning-derived physics framework.
### Interpretation
This image appears to be a conceptual diagram from a research paper or technical presentation regarding **Symbolic Regression** or **Automated Physics Discovery**.
The core argument is that complex physical systems can be decomposed into a set of primitive objects (spheres, springs, wedges) and primitive forces (spring force, surface gravity, universal gravitation). The system "discovers" the governing laws by toggling the $\delta_\lambda$ parameters. When the system observes an experiment (like a ball on a wedge), it automatically determines which potential energy terms are active (e.g., $\delta_g=1$ for gravity, $\delta_k=0$ for springs) and constructs the appropriate Lagrangian or force-balance equation. The "spontaneous instantiation" note implies an algorithmic process where the model identifies the relevant physics "on the fly" based on the visual or structural input of the experiment.
</details>
Figure 2: Schematic of tested experiments and main general laws discovered. Some complex configurations are omitted for clarity. See text for details.
Rediscovering Laws of Newtonian Mechanics. — To evaluate AI-Newton’s performance, we apply it to Newtonian mechanics problems, focusing on a set of 46 predefined experiments. These experiments involve three primary types of physical objects: balls (either small balls or celestial bodies), springs, and inclined planes. The experiments are designed to investigate both isolated and coupled systems, as illustrated in Fig. 2, including:
1. Free motion of individual balls and springs;
1. Elastic collision of balls;
1. Coupled systems demonstrating translational vibrations, rotational oscillations, and pendulum-like motions;
1. Gravity-related problems, such as projectile motion and motion on inclined planes, along with complex spring-ball systems;
1. Celestial mechanics problems involving gravitational interactions.
The complexities of experiments are systematically increased by varying the number of physical objects and spatial dimensions, encompassing high-degree-of-freedom problems such as coupled oscillations of chained 2-ball-2-spring systems on inclined planes, rotational dynamics of 4-ball-4-spring systems, and other complex configurations. To simulate realistic experimental conditions, all test data are generated by solving differential equations and incorporating Gaussian-distributed errors. This comprehensive experimental setup covers three types of forces in Newtonian mechanics, elastic forces, gravity near Earth’s surface, and universal gravitational forces, while incorporating realistic measurement uncertainties. In this way, it enables rigorous evaluation of AI-Newton’s capability to discover physical laws from noisy experimental data.
We evaluated the performance of our proof-of-concept implementation on an Intel Xeon Platinum 8370C (128 threads @ 3.500GHz) platform with NVIDIA A40 GPU, configured with 64 cores for parallel processing. With max trials set to 1200 and an average runtime of 48 hours, the system demonstrated robust knowledge discovery capabilities, identifying approximately 90 physical concepts and 50 general laws on average across the test cases. The discoveries include significant general laws such as energy conservation and Newton’s second law along with their relevant concepts, as shown in Fig. 2, providing complete explanatory for all experiments covering systems from simple to high-degree-of-freedom complex configurations.
<details>
<summary>knowledge_progression.png Details</summary>
### Visual Description
## Dot Plot: Distribution of Trials per Concept
### Overview
The image is a horizontal dot plot visualizing the "Number of trials" required for various "Concepts." The chart is divided into six vertical zones (labeled I through VI with faint Roman numerals) that segment the data based on the number of trials. Each concept is represented by a black dot indicating the mean or median value, with horizontal error bars representing the range or variance of the trials.
### Components/Axes
* **Y-Axis (Concepts):** Lists 14 distinct concepts, ordered from bottom to top: $m, v, k, g, a, T, P, V_k, V_g, F_k, F_g, G, V_G, F_G$.
* **X-Axis (Number of trials):** A linear scale ranging from 0 to 800+, with major tick marks every 100 units.
* **Zones:** The background is divided by vertical lines into six regions:
* **Zone I:** 0 to ~140
* **Zone II:** ~140 to ~200
* **Zone III:** ~200 to ~270
* **Zone IV:** ~270 to ~450
* **Zone V:** ~450 to ~650
* **Zone VI:** ~650 to 900+
### Detailed Analysis
The data points are distributed across the zones as follows (values are approximate):
| Concept | Zone | Approx. Mean/Center | Approx. Error Bar Range |
| :--- | :--- | :--- | :--- |
| **$m$** | I | 45 | 10 – 90 |
| **$v$** | I | 65 | 30 – 100 |
| **$k$** | I | 80 | 30 – 130 |
| **$g$** | III | 225 | 140 – 300 |
| **$a$** | III | 245 | 200 – 290 |
| **$T$** | IV | 310 | 280 – 340 |
| **$P$** | IV | 380 | 280 – 460 |
| **$V_k$** | IV | 390 | 310 – 480 |
| **$V_g$** | IV | 400 | 310 – 480 |
| **$F_k$** | V | 455 | 370 – 540 |
| **$F_g$** | V | 510 | 420 – 600 |
| **$G, V_G$** | VI | 740 | 640 – 840 |
| **$F_G$** | VI | 790 | 700 – 880 |
*Note: Zone II (140–200) contains no data points.*
### Key Observations
* **Progression:** There is a clear positive correlation between the listed concepts and the number of trials. As one moves up the Y-axis, the number of trials increases.
* **Clustering:** The concepts are grouped into distinct clusters. The most dense clustering occurs in Zone IV ($T, P, V_k, V_g$), where four concepts fall within a narrow range of ~310 to ~400 trials.
* **Variance:** The width of the error bars generally increases as the number of trials increases. Concepts with higher trial counts (e.g., $F_G$) exhibit significantly larger variance (error bars spanning ~180 units) compared to concepts with lower trial counts (e.g., $m$, spanning ~80 units).
* **Empty Zone:** Zone II is notably devoid of data, suggesting a "gap" in the complexity or trial requirements between the initial concepts ($m, v, k$) and the subsequent group ($g, a$).
### Interpretation
The data suggests a hierarchical structure in the complexity or difficulty of the concepts being measured. The "Number of trials" likely acts as a proxy for the computational or experimental effort required to resolve or verify each concept.
The progression from simple variables (like mass $m$ or velocity $v$) to more complex or derived variables (like forces $F_G$ or combined variables $G, V_G$) correlates strongly with an increased requirement for trials. The existence of distinct zones suggests that these concepts might be categorized into "difficulty tiers," where concepts within the same zone share similar experimental or computational requirements. The widening error bars at higher trial counts indicate that as the complexity of the concept increases, the uncertainty or variability in the number of trials required to reach a conclusion also increases significantly.
</details>
Figure 3: Statistical analysis of concept discovery timing on 10 test cases, recording the mean and standard deviation of discovery timings for key concepts. Number of trials means the number of analysis trial attempt has been done, not distinguishing which experiment. Roman numerals (I, II, …) in the background indicate the eras defined by the era-control strategy.
Statistical discovery progression on 10 test cases is illustrated in Fig. 3, showing the timing distribution of important concept discoveries. This discovery progression exhibits an incremental pattern, where AI-Newton first explores simple concepts (e.g., mass) before advancing to more complex ones (e.g., force). For instance, gravitational acceleration $g$ is defined as a constant by analyzing free-fall or projectile motion, where the vertical acceleration $a_{z}$ of the ball is invariant. In experiments with elastic collisions between balls, conservation of kinetic energy $T$ is discovered and proposed as a general law. Through plausible reasoning, elastic potential energy $V_{k}$ , gravitational potential energy near Earth’s surface $V_{g}$ , and universal gravitational potential energy $V_{G}$ are progressively defined when trying to apply the conservation of kinetic energy to inelastic experiments. These are then incorporated with kinetic energy conservation to ultimately formulate the complete law of energy conservation. The discovery of Newton’s second law follows an analogous progression: it is first proposed in a simple experimental context and then generalized through plausible reasoning.
It is important to emphasize that the system is able to independently discover and unify fundamental concepts from disparate physical contexts. For instance, AI-Newton can derive the concept of ‘mass’ through two distinct experimental routes: from the static elongation of a spring under gravity (defining gravitational mass, $m_{g}$ ) and from the experiment of a horizontal spring-mass oscillation system (defining inertial mass, $m_{i}$ ). Critically, the system then autonomously verify the numerical equivalence of $m_{g}$ and $m_{i}$ , effectively indicating a cornerstone of general relativity—the weak equivalence principle—from raw data alone.
Summary. — We introduce AI-Newton, a novel framework for the autonomous discovery of general physical laws from raw data across a large set of experiments, without supervision or pre-existing physical knowledge. This approach transcends current AI-driven methods, which are limited to extracting specific laws from individual experiments. Our main contributions are based on plausible reasoning, enabling us to: (1) propose physical concepts from the extracted laws; and (2) extend an existing general law by adding new terms, thereby adapting it to describe a wider range of experiments. Introducing interpretable physical concepts allows discovered laws to remain concise, making them more tractable for SR to identify. Furthermore, iteratively constructing general laws from existing ones enables a gradual, scalable discovery process. Applied to a large, noisy dataset of mechanics experiments, AI-Newton successfully rediscovers foundational laws, including Newton’s second law, the conservation of energy, and the law of universal gravitation. This work thus offers a promising pathway toward building AI systems capable of contributing to frontier scientific research.
As a first step, we employ AI-Newton to rediscover known physical laws—a task where direct reliance on large language models (LLMs) is unsuitable, as they already possess this knowledge. In future applications to frontier science, however, the DSL, the recommendation engine and the plausible reasoning components of the framework could be replaced or augmented by LLMs. This integration would grant the system direct access to all existing knowledge, enabling a more informed and efficient discovery process.
Acknowledgements. We would like to thank Hong-Fei Zhang for early participant of the project and many valuable discussions. This work is supported by the National Natural Science Foundation of China (No. 12325503), and the High-performance Computing Platform of Peking University.
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