Impact: Multi-Domain Evaluation

• Impact is a multifaceted concept defined by force interactions, research influence, and societal change, quantified across physics, bibliometrics, and AI.
• Quantification methods span dimensionless numbers, citation-based metrics, and composite indices that rigorously assess performance and outcomes.
• Applications include optimizing collision dynamics in engineering, evaluating research impact, and guiding policy and AI system design.

Impact is a central, multi-domain concept denoting forceful interactions in physics and engineering, quantitative influence in bibliometrics and research evaluation, and the realized effect or change—particularly long-term and societal—resulting from interventions or system outputs in fields such as AI, policy, and organizational management. Across these contexts, “impact” is precisely quantified using rigorous mathematical and statistical frameworks, and has become the backbone of comparative assessment, optimization, and real-world deployment in both the physical and information sciences.

1. Definitions and Contexts

Impact encompasses physical events (e.g., force transmission during a collision); statistical influence in scientometrics (e.g., citation metrics for research evaluation); measured societal or clinical outcomes (as in policy and healthcare); and, in computational systems, the end-to-end trace from technical outputs to meaningful real-world effects. Scholarly work distinguishes:

• Physical Impact: The mechanical response (force, stress, energy transfer) arising when bodies collide, often mediated by material, geometric, and dynamic properties (Ye et al., 8 Jan 2026).
• Research and Societal Impact: The measurable influence of research outputs on the scientific community (citations, shifting paradigms) or beyond (policy, public health) (Bornmann, 2014, Pan et al., 2013, Wagner et al., 2012).
• Impact in Computational, AI, and Engineering Systems: The degree to which outputs, decisions, or system behaviors cause observable, valued change, generally operationalized through multi-objective metrics, alignment with Theory of Change, or outcome-based evaluations (Kim, 9 Dec 2025).

2. Quantification of Impact: Metrics and Indicators

Quantitative measurement of impact depends on domain context.

Physical Sciences: Collisions and Impact Forces

Impact events are modeled using dimensionless groups such as the Weber ($\mathrm{We}$) and Ohnesorge ($\mathrm{Oh}$) numbers, and quantified by parameters including peak normalized force ($F_{p1}^*$), time-resolved force curves, and spatial spreading laws:

$$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$

where $F_{p1}$ is the primary force peak, $v_i$ is the impact velocity, $D_d$ droplet diameter (Ye et al., 8 Jan 2026).

Scientometrics: Author and Journal Impact

• Journal Impact Factor (JIF):

$$\mathrm{JIF}_X(t) = \frac{\text{Citations in year } t \text{ to journal } X \text{ papers }[t{-}2, t{-}1]}{\text{Number of citable items in } X \text{ during }[t{-}2, t{-}1]}$$

• Author Impact Factor (AIF) [Editor’s term]:

$$\mathrm{AIF}_A(t; \Delta t) = \frac{N_{c,A}(t,\Delta t)}{N_{p,A}(t,\Delta t)}$$

where $N_{c,A}(t,\Delta t)$ is citations in year $\mathrm{Oh}$0 to $\mathrm{Oh}$1’s papers from the previous $\mathrm{Oh}$2 years, and $\mathrm{Oh}$3 is the number of such papers (Pan et al., 2013).

• Integrated Impact Indicator ($\mathrm{Oh}$4):

$\mathrm{Oh}$5

where $\mathrm{Oh}$6 is the percentile rank of publication $\mathrm{Oh}$7 within its field/year. Allows aggregation from paper to author, institution, or nation, and supports nonparametric significance testing (Wagner et al., 2012).

Societal and Translational Impact

Frameworks sum contributions from multiple sources, e.g.: $\mathrm{Oh}$8 for weighted combinations of patent citations, clinical guideline citations, and altmetrics; parameters determined by policy priorities (Bornmann, 2014).

Engineering and AI: Impact-Driven Architecture

The Impact-Driven AI Framework (IDAIF) operationalizes impact as the attainment of multi-layered, often noncommensurate objectives aligned with Theory of Change, using multi-objective Pareto optimization:

$\mathrm{Oh}$9

where the objective is to minimize group-dependent risk $F_{p1}^*$0 under fairness and societal constraints (Kim, 9 Dec 2025).

3. Mechanistic and Statistical Modeling of Impact

Physical Impact Dynamics

Physical impact phenomena (e.g., droplet impact on cylindrical surfaces) are governed by interplay between inertia, capillarity, viscosity, and surface geometry, with impact force and spreading behaviors displaying power-law scaling with $F_{p1}^*$1 and $F_{p1}^*$2:

• Single-peak (deposition) vs. double-peak (rebound) force curve behavior.
• Scaling exponents for spreading area, angle, and asymmetry as functions of $F_{p1}^*$3 and $F_{p1}^*$4, extracted by fitting simulation or experimental data (Ye et al., 8 Jan 2026).

Impact Parameter Extraction in Experimental Physics

Neural network models predict the geometrical impact parameter $F_{p1}^*$5 in heavy-ion collisions from raw detector data:

$F_{p1}^*$6

High granularity in $F_{p1}^*$7 determination enhances precision in extracting collective flow and nuclear equation-of-state parameters (Wang et al., 2023).

4. Impact Measurement in Research Evaluation

Impact measurement in research is multidimensional. Principal approaches include:

• Citation-based indicators: JIF, AIF, $F_{p1}^*$8-index, MNCS, $F_{p1}^*$9, percentile-based rates (e.g., top-10% paper fraction).
• Altmetrics and web-based attention scores: Aggregate counts from social/web platforms, patents, clinical guidelines.
• Composite and field-normalized indicators: Adjust for field/career variations; e.g., dividing AIF by average field AIF.
• Qualitative and case-based rubrics: “Productive interactions” frameworks complement numerical metrics in capturing societal/policy impact (Bornmann, 2014).

Each metric exhibits biases—power-law distribution skew, susceptibility to gaming, lag effects, and field nonuniformity—that motivate the use of multiple complementary indicators (Pan et al., 2013, Bornmann, 2014, Wagner et al., 2012).

5. Applications Across Domains

Robotics and Manipulation

Impact informs both low-level control (e.g., forceful manipulation integrating internal-model predictive control and impedance control for variable object masses (Gao et al., 9 Jun 2026)) and high-level motion planning in clutter (balancing “acceptable” vs. critical collisions using Vision-LLM–derived semantic cost maps (Ling et al., 13 Mar 2025)).

Asteroid Impact Risk

Planetary defense workflows quantify impact risk using probabilistic (LOV-sampled) orbital predictions, mechanical effect models (overpressure, thermal, seismic, ejecta), and vulnerability-weighted exposure metrics to produce relative national or regional risk rankings. Population alone is a coarse proxy; only advanced physical modeling yields policy-relevant prioritization (Rumpf et al., 2016).

Safety and Structural Health Monitoring

Physics-informed learning frameworks integrate domain knowledge via architectural/inductive bias and physics-based constraints (e.g., kinetic energy conservation) to achieve robust impact identification from limited or noisy sensor data, with explicit losses: $$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$0 serving as consistency checks during inference (Marinho et al., 30 Mar 2026).

AI, Software Engineering, Policy, and Evaluation

Impact is operationalized in system design via Theory of Change, multi-objective optimization, outcome-based “ImpactOps,” and assurance frameworks. IDAIF defines full-stack architectural mapping from inputs to ultimate stakeholder impact, enforces normative/fairness constraints, and embeds impact tracing and outcome dashboards directly in the engineering lifecycle (Kim, 9 Dec 2025).

6. Limitations, Biases, and Future Developments

Impact assessment invariably faces intrinsic limitations:

• Temporal cutoffs (e.g., short $$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$1 in AIF) may underrepresent delayed “sleeping beauty” effects.
• Disciplinary nonuniformity and field-dependence in citation cultures, publication rates, and citation lag.
• Skew, randomness, and “blockbuster” effects dominate institutional/country-level indicator distributions (Bornmann, 2014).
• Gaming and predictability degrade indicator value under Goodhart’s Law.
• Interpretability and attribution in complex AI systems require explicit impact measurement at multiple levels (Kim, 9 Dec 2025).

Future research directions emphasize real-time, impact-aware architectures, field-normalized and fairness-robust bibliometric indicators, causal explanation and monitoring in AI, and robust physics-informed learning for impact event characterization.

7. Tabular Summary of Impact Indicators in Research Evaluation

Indicator	Definition/Formulation	Key Properties & Context
JIF	$$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$2	Journal-level, mean-based, field-dependent
h-index	$$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$3 papers with $$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$4 citations	Cumulative, insensitive to recency or low-impact work
AIF	$$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$5 (see above)	Author-level, dynamic, stiff to low-quality work, windowed
$$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$6	$$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$7 (percentiles)	Additive, nonparametric, flexible unit of analysis
SI (Soc. Impact)	$$F_{p1}^* = \frac{F_{p1}}{\rho v_i^2 D_d^2} = \beta_1 + \beta_2 \mathrm{We}^{-1}$$8	Composite, multi-source, policy-valued

Each of these metrics rests on domain-specific, theoretically grounded, and statistically rigorous quantification of “impact,” tailored to the requirements of comparative assessment, resource allocation, or scientific understanding within the respective field.